Skip to main content

2014 | OriginalPaper | Buchkapitel

6. Inverse Scattering Problems for Orthotropic Media

verfasst von : Fioralba Cakoni, David Colton

Erschienen in: A Qualitative Approach to Inverse Scattering Theory

Verlag: Springer US

Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter we extend the results of Chap. 4 to the case of the inverse scattering problem for an inhomogeneous orthotropic medium. The inverse problem we shall consider in this chapter is to determine the support of the orthotropic inhomogeneity given the far-field pattern of the scattered field for many incident directions.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
Reprinted from F. Cakoni, D. Colton, P. Monk, and J. Sun, The inverse electromagnetic scattering problem for anisotropic media, Inverse Problems 26 (2010), 074004.
 
Literatur
1.
Zurück zum Zitat Aktosun T, Gintides D, Papanicolaou V (2011) The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Problems 27:115004.MathSciNet Aktosun T, Gintides D, Papanicolaou V (2011) The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Problems 27:115004.MathSciNet
2.
Zurück zum Zitat Aktosun T, Papanicolaou V (2013) Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Problems 29:065007.MathSciNet Aktosun T, Papanicolaou V (2013) Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation. Inverse Problems 29:065007.MathSciNet
3.
Zurück zum Zitat Angell T, Kirsch A (1992) The conductive boundary condition for Maxwell’s equations. SIAM J. Appl. Math. 52:1597–1610.MathSciNetMATH Angell T, Kirsch A (1992) The conductive boundary condition for Maxwell’s equations. SIAM J. Appl. Math. 52:1597–1610.MathSciNetMATH
4.
Zurück zum Zitat Angell T, Kirsch A (2004) Optimization Methods in Electromagnetic Radiation. Springer, New York.MATH Angell T, Kirsch A (2004) Optimization Methods in Electromagnetic Radiation. Springer, New York.MATH
5.
Zurück zum Zitat Arens T (2001) Linear sampling methods for 2D inverse elastic wave scattering. Inverse Problems 17:1445–1464.MathSciNetMATH Arens T (2001) Linear sampling methods for 2D inverse elastic wave scattering. Inverse Problems 17:1445–1464.MathSciNetMATH
7.
Zurück zum Zitat Arens T, Lechleiter A(2009) The linear sampling method revisited. J. Integral Equations Appl. 21:179–203.MathSciNetMATH Arens T, Lechleiter A(2009) The linear sampling method revisited. J. Integral Equations Appl. 21:179–203.MathSciNetMATH
8.
Zurück zum Zitat Boas Jr, Ralph P (1954) Entire Functions. Academic, New York. Boas Jr, Ralph P (1954) Entire Functions. Academic, New York.
9.
Zurück zum Zitat Bonnet-BenDhia AS, Chesnel L, Haddar H (2011) On the use of t-coercivity to study the interior transmission eigenvalue problem. C. R. Acad. Sci., Ser. I 340:647–651.MathSciNet Bonnet-BenDhia AS, Chesnel L, Haddar H (2011) On the use of t-coercivity to study the interior transmission eigenvalue problem. C. R. Acad. Sci., Ser. I 340:647–651.MathSciNet
10.
Zurück zum Zitat Bonnet-BenDhia AS, Ciarlet P, Maria Zwölf C (2010) Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J. Comput. Appl. Math 234:1912–1919.MathSciNet Bonnet-BenDhia AS, Ciarlet P, Maria Zwölf C (2010) Time harmonic wave diffraction problems in materials with sign-shifting coefficients. J. Comput. Appl. Math 234:1912–1919.MathSciNet
11.
Zurück zum Zitat Bressan A (2013) Lecture Notes on Functional Analysis with Applications to Linear Partial Differential Equations. American Mathematical Society, Providence, RI.MATH Bressan A (2013) Lecture Notes on Functional Analysis with Applications to Linear Partial Differential Equations. American Mathematical Society, Providence, RI.MATH
12.
Zurück zum Zitat Buchanan JL, Gilbert RP, Wirgin A, Xu Y (2004) Marine Acoustics. Direct and Inverse Problems. SIAM, Philadelphia.MATH Buchanan JL, Gilbert RP, Wirgin A, Xu Y (2004) Marine Acoustics. Direct and Inverse Problems. SIAM, Philadelphia.MATH
13.
Zurück zum Zitat Cakoni F, Colton D (2003) A uniqueness theorem for an inverse electomagnetic scattering problem in inhomogeneous anisotropic media. Proc. Edinb. Math. Soc. 46:293–314.MathSciNetMATH Cakoni F, Colton D (2003) A uniqueness theorem for an inverse electomagnetic scattering problem in inhomogeneous anisotropic media. Proc. Edinb. Math. Soc. 46:293–314.MathSciNetMATH
14.
Zurück zum Zitat Cakoni F, Colton D (2003) On the mathematical basis of the linear sampling method. Georgian Math. J. 10/3:411–425. Cakoni F, Colton D (2003) On the mathematical basis of the linear sampling method. Georgian Math. J. 10/3:411–425.
15.
Zurück zum Zitat Cakoni F, Colton D (2003) The linear sampling method for cracks. Inverse Problems 19:279–295.MathSciNetMATH Cakoni F, Colton D (2003) The linear sampling method for cracks. Inverse Problems 19:279–295.MathSciNetMATH
16.
Zurück zum Zitat Cakoni F, Colton D (2003) Combined far field operators in electromagnetic inverse scattering theory. Math. Methods Appl. Sci. 26:413–429.MathSciNetMATH Cakoni F, Colton D (2003) Combined far field operators in electromagnetic inverse scattering theory. Math. Methods Appl. Sci. 26:413–429.MathSciNetMATH
17.
Zurück zum Zitat Cakoni F, Colton D (2004) The determination of the surface impedance of a partially coated obstacle from far field data. SIAM J. Appl. Math. 64:709–723.MathSciNetMATH Cakoni F, Colton D (2004) The determination of the surface impedance of a partially coated obstacle from far field data. SIAM J. Appl. Math. 64:709–723.MathSciNetMATH
18.
Zurück zum Zitat Cakoni F, Colton D (2005) Open problems in the qualitative approach to inverse electromagnetic scattering theory. Eur. J. Appl. Math. to appear. Cakoni F, Colton D (2005) Open problems in the qualitative approach to inverse electromagnetic scattering theory. Eur. J. Appl. Math. to appear.
19.
Zurück zum Zitat Cakoni F, Colton D, Gintides D (2010) The interior transmission eigenvalue problem. SIAM J. Math. Anal. 42:2912–2921.MathSciNetMATH Cakoni F, Colton D, Gintides D (2010) The interior transmission eigenvalue problem. SIAM J. Math. Anal. 42:2912–2921.MathSciNetMATH
20.
Zurück zum Zitat Cakoni F, Colton D, Haddar H (2002) The linear sampling method for anisotropic media. J. Comp. Appl. Math. 146:285–299.MathSciNetMATH Cakoni F, Colton D, Haddar H (2002) The linear sampling method for anisotropic media. J. Comp. Appl. Math. 146:285–299.MathSciNetMATH
21.
Zurück zum Zitat Cakoni F, Colton D, Haddar H (2009) The computation of lower bounds for the norm of the index of refraction in an anisotropic media. J. Integral Equations Appl. 21(2):203–227.MathSciNetMATH Cakoni F, Colton D, Haddar H (2009) The computation of lower bounds for the norm of the index of refraction in an anisotropic media. J. Integral Equations Appl. 21(2):203–227.MathSciNetMATH
22.
Zurück zum Zitat Cakoni F, Colton D, Haddar H (2010) On the determination of Dirichlet or transmission eigenvalues from far field data. C. R. Math. Acad. Sci. Paris, Ser I 348(7–8):379–383.MathSciNetMATH Cakoni F, Colton D, Haddar H (2010) On the determination of Dirichlet or transmission eigenvalues from far field data. C. R. Math. Acad. Sci. Paris, Ser I 348(7–8):379–383.MathSciNetMATH
23.
Zurück zum Zitat Cakoni F, Colton D, Monk P (2001) The direct and inverse scattering problems for partially coated obstacles. Inverse Problems 17:1997–2015.MathSciNetMATH Cakoni F, Colton D, Monk P (2001) The direct and inverse scattering problems for partially coated obstacles. Inverse Problems 17:1997–2015.MathSciNetMATH
24.
Zurück zum Zitat Cakoni F, Colton D, Monk P (2004) The electromagnetic inverse scattering problem for partly coated Lipschitz domains. Proc. R. Soc. Edinb. 134A:661–682.MathSciNet Cakoni F, Colton D, Monk P (2004) The electromagnetic inverse scattering problem for partly coated Lipschitz domains. Proc. R. Soc. Edinb. 134A:661–682.MathSciNet
25.
Zurück zum Zitat Cakoni F, Colton D, Monk P (2010) The determination of boundary coefficients from far field measurements. J. Int. Equations Appl. 42(2):167–191.MathSciNet Cakoni F, Colton D, Monk P (2010) The determination of boundary coefficients from far field measurements. J. Int. Equations Appl. 42(2):167–191.MathSciNet
26.
Zurück zum Zitat Cakoni F, Colton D, Monk P (2011) The Linear Sampling Method in Inverse Electromagnetic Scattering. CBMS-NSF Regional Conference Series in Applied Mathematics 80, SIAM, Philadelphia. Cakoni F, Colton D, Monk P (2011) The Linear Sampling Method in Inverse Electromagnetic Scattering. CBMS-NSF Regional Conference Series in Applied Mathematics 80, SIAM, Philadelphia.
27.
Zurück zum Zitat Cakoni F, Colton D, Monk P (2005) The determination of the surface conductivity of a partially coated dielectric. SIAM J. Appl. Math. 65:767–789.MathSciNetMATH Cakoni F, Colton D, Monk P (2005) The determination of the surface conductivity of a partially coated dielectric. SIAM J. Appl. Math. 65:767–789.MathSciNetMATH
28.
Zurück zum Zitat Cakoni F, Colton D, Monk P, Sun J (2010) The inverse electromagnetic scattering problem for anisotropic media. Inverse Problems 26:074004.MathSciNet Cakoni F, Colton D, Monk P, Sun J (2010) The inverse electromagnetic scattering problem for anisotropic media. Inverse Problems 26:074004.MathSciNet
29.
Zurück zum Zitat Cakoni F, Darrigrand E (2005) The inverse electromagnetic scattering problem for a mixed boundary value problem for screens. J. Comp. Appl. Math. 174:251–269.MathSciNetMATH Cakoni F, Darrigrand E (2005) The inverse electromagnetic scattering problem for a mixed boundary value problem for screens. J. Comp. Appl. Math. 174:251–269.MathSciNetMATH
30.
Zurück zum Zitat Cakoni F, Fares M, Haddar H (2006) Anals of two linear sampling methods applied to electromagnetic imaging of buried objects. Inverse Problems 42:237–255.MathSciNet Cakoni F, Fares M, Haddar H (2006) Anals of two linear sampling methods applied to electromagnetic imaging of buried objects. Inverse Problems 42:237–255.MathSciNet
31.
Zurück zum Zitat Cakoni F, Gintides D, Haddar H (2010) The existence of an infinite discrete set of transmission eigenvalues. SIAM J. Math. Anal. 42:237–255.MathSciNetMATH Cakoni F, Gintides D, Haddar H (2010) The existence of an infinite discrete set of transmission eigenvalues. SIAM J. Math. Anal. 42:237–255.MathSciNetMATH
32.
Zurück zum Zitat Cakoni F, Haddar H (2013) Transmission eigenvalues in inverse scattering theory Inverse Problems and Applications, Inside Out 60, MSRI Publications, Berkeley, CA. Cakoni F, Haddar H (2013) Transmission eigenvalues in inverse scattering theory Inverse Problems and Applications, Inside Out 60, MSRI Publications, Berkeley, CA.
33.
Zurück zum Zitat Cakoni F, Haddar H (2008), On the existence of transmission eigenvalues in an inhomogeneous medium. Applicable Anal. 88(4):475–493.MathSciNet Cakoni F, Haddar H (2008), On the existence of transmission eigenvalues in an inhomogeneous medium. Applicable Anal. 88(4):475–493.MathSciNet
34.
Zurück zum Zitat Cakoni F, Haddar H (2003) Interior transmission problem for anisotropic media. Mathematical and Numerical Aspects of Wave Propagation (Cohen et al., eds.), Springer, 613–618. Cakoni F, Haddar H (2003) Interior transmission problem for anisotropic media. Mathematical and Numerical Aspects of Wave Propagation (Cohen et al., eds.), Springer, 613–618.
35.
Zurück zum Zitat Cakoni F, Kirsch A (2010) On the interior transmission eigenvalue problem (2010) Int. J. Comp. Sci. Math. 3:142–167.MathSciNetMATH Cakoni F, Kirsch A (2010) On the interior transmission eigenvalue problem (2010) Int. J. Comp. Sci. Math. 3:142–167.MathSciNetMATH
36.
Zurück zum Zitat Chanillo S, Helffer B, Laptev A (2004) Nonlinear eigenvalues and analytic hypoellipticity. J. Functional Analysis 209:425–443.MathSciNetMATH Chanillo S, Helffer B, Laptev A (2004) Nonlinear eigenvalues and analytic hypoellipticity. J. Functional Analysis 209:425–443.MathSciNetMATH
37.
Zurück zum Zitat Charalambopoulos A, Gintides D, Kiriaki K (2002) The linear sampling method for the transmission problem in three-dimensional linear elasticity. Inverse Problems 18:547–558.MathSciNetMATH Charalambopoulos A, Gintides D, Kiriaki K (2002) The linear sampling method for the transmission problem in three-dimensional linear elasticity. Inverse Problems 18:547–558.MathSciNetMATH
38.
Zurück zum Zitat Charalambopoulos A, Gintides D, Kiriaki K (2003) The linear sampling method for non-absorbing penetrable elastic bodies. Inverse Problems 19:549–561.MathSciNetMATH Charalambopoulos A, Gintides D, Kiriaki K (2003) The linear sampling method for non-absorbing penetrable elastic bodies. Inverse Problems 19:549–561.MathSciNetMATH
39.
Zurück zum Zitat Chesnel L (2012) Étude de quelques problémes de transmission avec changement de signe. Application aux métamatériaux. Ph.D. thesis. École Doctorale de l’École Polytechnique, France. Chesnel L (2012) Étude de quelques problémes de transmission avec changement de signe. Application aux métamatériaux. Ph.D. thesis. École Doctorale de l’École Polytechnique, France.
40.
Zurück zum Zitat Chesnel L (2012) Interior transmission eigenvalue problem for Maxwell’s equations: the T-coercivity as an alternative approach. Inverse Problems 28:065005.MathSciNet Chesnel L (2012) Interior transmission eigenvalue problem for Maxwell’s equations: the T-coercivity as an alternative approach. Inverse Problems 28:065005.MathSciNet
41.
Zurück zum Zitat Cheng J, Yamamoto M (2003) Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves. Inverse Problems 19:1361–1384.MathSciNet Cheng J, Yamamoto M (2003) Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves. Inverse Problems 19:1361–1384.MathSciNet
42.
Zurück zum Zitat Collino F, Fares M, Haddar H (2003) Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems. Inverse Problems 19:1279–1298.MathSciNetMATH Collino F, Fares M, Haddar H (2003) Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems. Inverse Problems 19:1279–1298.MathSciNetMATH
43.
Zurück zum Zitat Colton D (2004) Partial Differential Equations: An Introduction. Dover, New York. Colton D (2004) Partial Differential Equations: An Introduction. Dover, New York.
44.
Zurück zum Zitat Colton D, Coyle J, Monk P (2000) Recent developments in inverse acoustic scattering theory. SIAM Rev. 42:369–414.MathSciNetMATH Colton D, Coyle J, Monk P (2000) Recent developments in inverse acoustic scattering theory. SIAM Rev. 42:369–414.MathSciNetMATH
45.
Zurück zum Zitat Colton D (1980) Analytic Theory of Partial Differential Equations. Pitman Advanced Publishing Program, Boston.MATH Colton D (1980) Analytic Theory of Partial Differential Equations. Pitman Advanced Publishing Program, Boston.MATH
46.
Zurück zum Zitat Colton D, Erbe C (1996) Spectral theory of the magnetic far field operator in an orthotropic medium, in Nonlinear Problems in Applied Mathematics, SIAM, Philadelphia. Colton D, Erbe C (1996) Spectral theory of the magnetic far field operator in an orthotropic medium, in Nonlinear Problems in Applied Mathematics, SIAM, Philadelphia.
47.
Zurück zum Zitat Colton D, Haddar H (2005) An application of the reciprocity gap functional to inverse scattering theory. Inverse Problems 21:383–398.MathSciNetMATH Colton D, Haddar H (2005) An application of the reciprocity gap functional to inverse scattering theory. Inverse Problems 21:383–398.MathSciNetMATH
48.
Zurück zum Zitat Colton D, Haddar H, Monk P (2002) The linear sampling method for solving the electromagnetic inverse scattering problem. SIAM J. Sci. Comput. 24:719–731.MathSciNetMATH Colton D, Haddar H, Monk P (2002) The linear sampling method for solving the electromagnetic inverse scattering problem. SIAM J. Sci. Comput. 24:719–731.MathSciNetMATH
49.
Zurück zum Zitat Colton D, Haddar H, Piana P (2003) The linear sampling method in inverse electromagnetic scattering theory. Inverse Problems 19:S105–S137.MathSciNetMATH Colton D, Haddar H, Piana P (2003) The linear sampling method in inverse electromagnetic scattering theory. Inverse Problems 19:S105–S137.MathSciNetMATH
50.
Zurück zum Zitat Colton D, Kirsch A (1996) A simple method for solving inverse scattering problems in the resonance region. Inverse Problems 12:383–393.MathSciNetMATH Colton D, Kirsch A (1996) A simple method for solving inverse scattering problems in the resonance region. Inverse Problems 12:383–393.MathSciNetMATH
51.
Zurück zum Zitat Colton D, Kress R (1983) Integral Equation Methods in Scattering Theory. Wiley, New York.MATH Colton D, Kress R (1983) Integral Equation Methods in Scattering Theory. Wiley, New York.MATH
52.
Zurück zum Zitat Colton D, Kress R (1995) Eigenvalues of the far field operator and inverse scattering theory. SIAM J. Math. Anal. 26:601–615.MathSciNetMATH Colton D, Kress R (1995) Eigenvalues of the far field operator and inverse scattering theory. SIAM J. Math. Anal. 26:601–615.MathSciNetMATH
53.
Zurück zum Zitat Colton D, Kress R (1995) Eigenvalues of the far field operator for the Helmholtz equation in an absorbing medium. SIAM J. Appl. Math. 55:1724–35.MathSciNetMATH Colton D, Kress R (1995) Eigenvalues of the far field operator for the Helmholtz equation in an absorbing medium. SIAM J. Appl. Math. 55:1724–35.MathSciNetMATH
54.
Zurück zum Zitat Colton D, Kress R (2013) Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edn. Springer, New York.MATH Colton D, Kress R (2013) Inverse Acoustic and Electromagnetic Scattering Theory, 3rd edn. Springer, New York.MATH
55.
Zurück zum Zitat Colton D, Kress R (2001) On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces. Math. Methods Appl. Sci. 24:1289–1303.MathSciNetMATH Colton D, Kress R (2001) On the denseness of Herglotz wave functions and electromagnetic Herglotz pairs in Sobolev spaces. Math. Methods Appl. Sci. 24:1289–1303.MathSciNetMATH
56.
Zurück zum Zitat Colton D, Leung YJ (2013) Complex eigenvalues and the inverse spectral problem for transmission eigenvalues. Inverse Problems. 29:104008. Colton D, Leung YJ (2013) Complex eigenvalues and the inverse spectral problem for transmission eigenvalues. Inverse Problems. 29:104008.
57.
Zurück zum Zitat Colton D, Kress R, Monk P. (1997) Inverse scattering from an orthotropic medium. J. Comp. Appl. Math. 81:269–298.MathSciNetMATH Colton D, Kress R, Monk P. (1997) Inverse scattering from an orthotropic medium. J. Comp. Appl. Math. 81:269–298.MathSciNetMATH
58.
Zurück zum Zitat Colton D, Monk P. (1999) A linear sampling method for the detection of leukemia using microwaves. II. SIAM J. Appl. Math. 69, 241–255. Colton D, Monk P. (1999) A linear sampling method for the detection of leukemia using microwaves. II. SIAM J. Appl. Math. 69, 241–255.
59.
Zurück zum Zitat Colton D, Päivarinta L (1992) The uniqueness of a solution to an inverse scattering problem for electromagnetic wave. Arch. Rational Mech. Anal. 119:59–70.MathSciNetMATH Colton D, Päivarinta L (1992) The uniqueness of a solution to an inverse scattering problem for electromagnetic wave. Arch. Rational Mech. Anal. 119:59–70.MathSciNetMATH
60.
Zurück zum Zitat Colton D, Päivärinta L, Sylvester J (2007) The interior transmission problem. Inverse Problems Imag. 1:13–28.MATH Colton D, Päivärinta L, Sylvester J (2007) The interior transmission problem. Inverse Problems Imag. 1:13–28.MATH
61.
Zurück zum Zitat Colton D, Piana M, Potthast R (1997) A simple method using Morozov’s discrepancy principle for solving inverse scattering problems. Inverse Problems 13:1477–1493.MathSciNetMATH Colton D, Piana M, Potthast R (1997) A simple method using Morozov’s discrepancy principle for solving inverse scattering problems. Inverse Problems 13:1477–1493.MathSciNetMATH
62.
Zurück zum Zitat Colton D, Sleeman BD (1983) Uniqueness theorems for the inverse problem of acoustic scattering. IMA J. Appl. Math. 31:253–59.MathSciNetMATH Colton D, Sleeman BD (1983) Uniqueness theorems for the inverse problem of acoustic scattering. IMA J. Appl. Math. 31:253–59.MathSciNetMATH
63.
Zurück zum Zitat Colton D, Sleeman BD (2001) An approximation property of importance in inverse scattering theory. Proc. Edinb. Math. Soc. 44:449–454.MathSciNetMATH Colton D, Sleeman BD (2001) An approximation property of importance in inverse scattering theory. Proc. Edinb. Math. Soc. 44:449–454.MathSciNetMATH
64.
Zurück zum Zitat Costabel M, Dauge M (2002) Crack singularities for general elliptic systems. Math. Nachr. 235:29–49.MathSciNetMATH Costabel M, Dauge M (2002) Crack singularities for general elliptic systems. Math. Nachr. 235:29–49.MathSciNetMATH
65.
Zurück zum Zitat Costabel M, Dauge M (1996) A singularly perturbed mixed boundary value problem. Comm. Partial Differential Equations 21:1919–1949.MathSciNetMATH Costabel M, Dauge M (1996) A singularly perturbed mixed boundary value problem. Comm. Partial Differential Equations 21:1919–1949.MathSciNetMATH
66.
Zurück zum Zitat Cossonnière A, Haddar H (2011) The electromagnetic interior transmission problem for regions with cavities. SIAM J. Math. Anal. 43:1698–1715.MathSciNetMATH Cossonnière A, Haddar H (2011) The electromagnetic interior transmission problem for regions with cavities. SIAM J. Math. Anal. 43:1698–1715.MathSciNetMATH
67.
Zurück zum Zitat Coyle J (2000) An inverse electromagnetic scattering problem in a two-layered background. Inverse Problems 16:275–292.MathSciNetMATH Coyle J (2000) An inverse electromagnetic scattering problem in a two-layered background. Inverse Problems 16:275–292.MathSciNetMATH
68.
Zurück zum Zitat Engl HW, Hanke M, Neubauer A (1996) Regularization of Inverse Problems. Kluwer, Dordrecht.MATH Engl HW, Hanke M, Neubauer A (1996) Regularization of Inverse Problems. Kluwer, Dordrecht.MATH
69.
70.
Zurück zum Zitat Friedman A (1969) Partial Differential Equations. Holt, Rinehart and Winston, New York.MATH Friedman A (1969) Partial Differential Equations. Holt, Rinehart and Winston, New York.MATH
71.
Zurück zum Zitat Ghosh Roy DN, Couchman LS (2002) Inverse Problems and Inverse Scattering of Plane Waves. Academic, London. Ghosh Roy DN, Couchman LS (2002) Inverse Problems and Inverse Scattering of Plane Waves. Academic, London.
72.
Zurück zum Zitat Gilbarg D, Trudinger NS (1983) Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, Berlin.MATH Gilbarg D, Trudinger NS (1983) Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, Berlin.MATH
73.
Zurück zum Zitat Gintides D, Kiriaki K (2001) The far-field equations in linear elasticity – an inversion scheme. Z. Angew. Math. Mech. 81:305–316.MathSciNetMATH Gintides D, Kiriaki K (2001) The far-field equations in linear elasticity – an inversion scheme. Z. Angew. Math. Mech. 81:305–316.MathSciNetMATH
74.
Zurück zum Zitat Griesmaier R, Hanke M, Sylvester J (to appear) Far field splitting for the Helmholtz equation. Griesmaier R, Hanke M, Sylvester J (to appear) Far field splitting for the Helmholtz equation.
75.
Zurück zum Zitat Grinberg NI, Kirsch A (2002) The linear sampling method in inverse obstacle scattering for impedance boundary conditions. J. Inv. Ill-Posed Problems 10:171–185.MathSciNetMATH Grinberg NI, Kirsch A (2002) The linear sampling method in inverse obstacle scattering for impedance boundary conditions. J. Inv. Ill-Posed Problems 10:171–185.MathSciNetMATH
76.
Zurück zum Zitat Grinberg NI, Kirsch A (2004) The factorization method for obstacles with a-priori separated sound-soft and sound-hard parts. Math. Comput. Simulation 66:267–279MathSciNetMATH Grinberg NI, Kirsch A (2004) The factorization method for obstacles with a-priori separated sound-soft and sound-hard parts. Math. Comput. Simulation 66:267–279MathSciNetMATH
77.
Zurück zum Zitat Gylys-Colwell F (1996) An inverse problem for the Helmholtz equation. Inverse Problems 12:139–156.MathSciNetMATH Gylys-Colwell F (1996) An inverse problem for the Helmholtz equation. Inverse Problems 12:139–156.MathSciNetMATH
78.
Zurück zum Zitat Haddar H (2004) The interior transmission problem for anisotropic Maxwell’s equations and its applications to the inverse problem. Math. Methods Appl. Sci. 27:2111–2129.MathSciNetMATH Haddar H (2004) The interior transmission problem for anisotropic Maxwell’s equations and its applications to the inverse problem. Math. Methods Appl. Sci. 27:2111–2129.MathSciNetMATH
79.
Zurück zum Zitat Haddar H, Joly P (2002)Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings. J. Comp. Appl. Math. 143:201–236.MathSciNetMATH Haddar H, Joly P (2002)Stability of thin layer approximation of electromagnetic waves scattering by linear and nonlinear coatings. J. Comp. Appl. Math. 143:201–236.MathSciNetMATH
80.
Zurück zum Zitat Haddar H, Monk P (2002) The linear sampling method for solving the electromagnetic inverse medium problem. Inverse Problems 18:891–906.MathSciNetMATH Haddar H, Monk P (2002) The linear sampling method for solving the electromagnetic inverse medium problem. Inverse Problems 18:891–906.MathSciNetMATH
81.
Zurück zum Zitat Hähner P (2000) On the uniqueness of the shape of a penetrable, anisotropic obstacle. J. Comp. Appl. Math. 116:167–180.MATH Hähner P (2000) On the uniqueness of the shape of a penetrable, anisotropic obstacle. J. Comp. Appl. Math. 116:167–180.MATH
82.
Zurück zum Zitat Hähner P (2002) Electromagnetic wave scattering: theory. in Scattering (Pike and Sabatier, eds.) Academic, New York. Hähner P (2002) Electromagnetic wave scattering: theory. in Scattering (Pike and Sabatier, eds.) Academic, New York.
83.
Zurück zum Zitat Hartman P, Wilcox C (1961) On solutions of the Helmholtz equation in exterior domains. Math. Zeit. 75:228–255.MathSciNetMATH Hartman P, Wilcox C (1961) On solutions of the Helmholtz equation in exterior domains. Math. Zeit. 75:228–255.MathSciNetMATH
84.
Zurück zum Zitat Hitrik M, Krupchyk K, Ola P, Päivärinta L (2010) Transmission eigenvalues for operators with constant coefficients. SIAM J. Math. Anal. 42:2965–2986.MathSciNetMATH Hitrik M, Krupchyk K, Ola P, Päivärinta L (2010) Transmission eigenvalues for operators with constant coefficients. SIAM J. Math. Anal. 42:2965–2986.MathSciNetMATH
85.
Zurück zum Zitat Hitrik M, Krupchyk K, Ola P and Päivärinta L (2011) The interior transmission problem and bounds on transmission eigenvalues. Math Res. Lett. 18:279–293.MathSciNetMATH Hitrik M, Krupchyk K, Ola P and Päivärinta L (2011) The interior transmission problem and bounds on transmission eigenvalues. Math Res. Lett. 18:279–293.MathSciNetMATH
86.
Zurück zum Zitat Hitrik M, Krupchyk K, Ola P, Päivärinta L (2011) Transmission eigenvalues for elliptic operators. SIAM J. Math. Anal. 43:2630–2639.MathSciNetMATH Hitrik M, Krupchyk K, Ola P, Päivärinta L (2011) Transmission eigenvalues for elliptic operators. SIAM J. Math. Anal. 43:2630–2639.MathSciNetMATH
87.
Zurück zum Zitat Hochstadt H (1973) Integral Equations. Wiley, New York.MATH Hochstadt H (1973) Integral Equations. Wiley, New York.MATH
88.
Zurück zum Zitat Hooper AE, Hambric HN (1999) Unexploded ordinance (UXO): The problem. Detection and Identification of Visually Obscured Targets (Baum, ed.), Taylor and Francis, Philadelphia. Hooper AE, Hambric HN (1999) Unexploded ordinance (UXO): The problem. Detection and Identification of Visually Obscured Targets (Baum, ed.), Taylor and Francis, Philadelphia.
89.
Zurück zum Zitat Hörmander L (1985) The Analysis of Linear Partial Differential Operators III. Springer, Berlin.MATH Hörmander L (1985) The Analysis of Linear Partial Differential Operators III. Springer, Berlin.MATH
90.
Zurück zum Zitat Hsiao G, Wendland WL (2008) Boundary Integral Equations. Springer, Berlin.MATH Hsiao G, Wendland WL (2008) Boundary Integral Equations. Springer, Berlin.MATH
91.
Zurück zum Zitat Ikehata M (1998) Reconstruction of the shape of an obstacle from scattering amplitude at a fixed frequency. Inverse Problems 14:949–954.MathSciNetMATH Ikehata M (1998) Reconstruction of the shape of an obstacle from scattering amplitude at a fixed frequency. Inverse Problems 14:949–954.MathSciNetMATH
92.
Zurück zum Zitat Ikehata M (1999) Reconstructions of obstacle from boundary measurements. Waves Motion 30:205–223.MathSciNetMATH Ikehata M (1999) Reconstructions of obstacle from boundary measurements. Waves Motion 30:205–223.MathSciNetMATH
93.
Zurück zum Zitat Isakov V (1988) On the uniqueness in the inverse transmission scattering problem. Comm. Partial Differential Equations 15:1565–1587.MathSciNet Isakov V (1988) On the uniqueness in the inverse transmission scattering problem. Comm. Partial Differential Equations 15:1565–1587.MathSciNet
94.
Zurück zum Zitat Isakov V (1998) Inverse Problems for Partial Differential Equations. Springer, New York.MATH Isakov V (1998) Inverse Problems for Partial Differential Equations. Springer, New York.MATH
95.
Zurück zum Zitat John F (1982) Partial Differential Equations, 4th ed. Springer Verlag, New York.MATH John F (1982) Partial Differential Equations, 4th ed. Springer Verlag, New York.MATH
96.
Zurück zum Zitat Jones DS (1974) Integral equations for the exterior acoustic problem. Q. J. Mech. Appl. Math. 27:129–142.MATH Jones DS (1974) Integral equations for the exterior acoustic problem. Q. J. Mech. Appl. Math. 27:129–142.MATH
97.
Zurück zum Zitat Y. Katznelson (9168) An Introduction to Harmonic Analysis. Wiley, New York. Y. Katznelson (9168) An Introduction to Harmonic Analysis. Wiley, New York.
98.
Zurück zum Zitat Kirsch A (2011) An Introduction to the Mathematical Theory of Inverse Problems, 2nd edn. Springer, New York.MATH Kirsch A (2011) An Introduction to the Mathematical Theory of Inverse Problems, 2nd edn. Springer, New York.MATH
99.
Zurück zum Zitat Kirsch A (1998) Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Problems 14:1489–1512.MathSciNetMATH Kirsch A (1998) Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Problems 14:1489–1512.MathSciNetMATH
100.
Zurück zum Zitat Kirsch A (1999) Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory. Inverse Problems 15:413–29.MathSciNetMATH Kirsch A (1999) Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory. Inverse Problems 15:413–29.MathSciNetMATH
101.
Zurück zum Zitat Kirsch A (2002) The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media. Inverse Problems 18:1025–1040.MathSciNetMATH Kirsch A (2002) The MUSIC-algorithm and the factorization method in inverse scattering theory for inhomogeneous media. Inverse Problems 18:1025–1040.MathSciNetMATH
102.
Zurück zum Zitat Kirsch A (2004) The factorization method for Maxwell’s equations. Inverse Problems 20:S117-S134.MathSciNetMATH Kirsch A (2004) The factorization method for Maxwell’s equations. Inverse Problems 20:S117-S134.MathSciNetMATH
103.
Zurück zum Zitat Kirsch A (2005) The factorization method for a class of inverse elliptic problems. Math. Nachr. 278:258–277.MathSciNetMATH Kirsch A (2005) The factorization method for a class of inverse elliptic problems. Math. Nachr. 278:258–277.MathSciNetMATH
104.
Zurück zum Zitat Kirsch A (2008) An integral equation for the scattering problem for an anisotropic medium and the factorization method. Advanced Topics in Scattering and Biomedical Engineering, Proceedings of the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering. World Scientific, New Jersey. Kirsch A (2008) An integral equation for the scattering problem for an anisotropic medium and the factorization method. Advanced Topics in Scattering and Biomedical Engineering, Proceedings of the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering. World Scientific, New Jersey.
105.
Zurück zum Zitat Kirsch A (2009) On the existence of transmission eigenvalues. Inverse Problems Imag. 3:155–172.MathSciNetMATH Kirsch A (2009) On the existence of transmission eigenvalues. Inverse Problems Imag. 3:155–172.MathSciNetMATH
106.
Zurück zum Zitat Kirsch A, Kress R (1993) Uniqueness in inverse obstacle scattering. Inverse Problems 9:81–96.MathSciNetMATH Kirsch A, Kress R (1993) Uniqueness in inverse obstacle scattering. Inverse Problems 9:81–96.MathSciNetMATH
107.
Zurück zum Zitat Kirsch A, Grinberg N (2008) The Factorization Method for Inverse Problems. Oxford University Press, Oxford.MATH Kirsch A, Grinberg N (2008) The Factorization Method for Inverse Problems. Oxford University Press, Oxford.MATH
108.
Zurück zum Zitat Kirsch A, Ritter S (2000) A linear sampling method for inverse scattering from an open arc. Inverse Problems 16:89–105.MathSciNetMATH Kirsch A, Ritter S (2000) A linear sampling method for inverse scattering from an open arc. Inverse Problems 16:89–105.MathSciNetMATH
109.
Zurück zum Zitat Kleinman RE, Roach GF (1982) On modified Green’s functions in exterior problems for the Helmholtz equation. Proc. R. Soc. Lond. A383:313–332.MathSciNet Kleinman RE, Roach GF (1982) On modified Green’s functions in exterior problems for the Helmholtz equation. Proc. R. Soc. Lond. A383:313–332.MathSciNet
110.
111.
Zurück zum Zitat Kress R (1999) Linear Integral Equations, 2nd edn. Springer, New York.MATH Kress R (1999) Linear Integral Equations, 2nd edn. Springer, New York.MATH
112.
Zurück zum Zitat Kress R, Lee KM (2003) Integral equation methods for scattering from an impedance crack. J. Comp. Appl. Math. 161:161–177.MathSciNetMATH Kress R, Lee KM (2003) Integral equation methods for scattering from an impedance crack. J. Comp. Appl. Math. 161:161–177.MathSciNetMATH
113.
Zurück zum Zitat Kress R, Rundell W (2001) Inverse scattering for shape and impedance. Inverse Problems 17:1075–1085.MathSciNetMATH Kress R, Rundell W (2001) Inverse scattering for shape and impedance. Inverse Problems 17:1075–1085.MathSciNetMATH
114.
Zurück zum Zitat Kress R, Serranho P (2005) A hybrid method for two-dimensional crack reconstruction. Inverse Problems 21:773–784.MathSciNetMATH Kress R, Serranho P (2005) A hybrid method for two-dimensional crack reconstruction. Inverse Problems 21:773–784.MathSciNetMATH
115.
Zurück zum Zitat Kreyszig E (1978) Introductory Functional Analysis with Applications. Wiley, New York.MATH Kreyszig E (1978) Introductory Functional Analysis with Applications. Wiley, New York.MATH
116.
117.
Zurück zum Zitat Kusiak S, Sylvester J (2005) The convex scattering support in a background medium. SIAM J. Math. Anal. 36:1142–1158.MathSciNetMATH Kusiak S, Sylvester J (2005) The convex scattering support in a background medium. SIAM J. Math. Anal. 36:1142–1158.MathSciNetMATH
118.
Zurück zum Zitat Lakshtanov E, Vainberg B (2012) Bounds on positive interior transmission eigenvalues. Inverse Problems 28:105005.MathSciNet Lakshtanov E, Vainberg B (2012) Bounds on positive interior transmission eigenvalues. Inverse Problems 28:105005.MathSciNet
119.
Zurück zum Zitat Lakshtanov E, Vainberg B (2012) Remarks on interior transmission eigenvalues, Weyl formula and branching billiards. J. Phys. A 25 12:125202. Lakshtanov E, Vainberg B (2012) Remarks on interior transmission eigenvalues, Weyl formula and branching billiards. J. Phys. A 25 12:125202.
120.
Zurück zum Zitat Lakshtanov E, Vainberg B (2012) Ellipticity in the interior transmission problem in anisotropic media. SIAM J. Math. Anal. 44 2:1165–1174.MathSciNetMATH Lakshtanov E, Vainberg B (2012) Ellipticity in the interior transmission problem in anisotropic media. SIAM J. Math. Anal. 44 2:1165–1174.MathSciNetMATH
121.
Zurück zum Zitat Lebedev NN (1965) Special Functions and Their Applications. Prentice-Hall, Englewood Cliffs, NJ.MATH Lebedev NN (1965) Special Functions and Their Applications. Prentice-Hall, Englewood Cliffs, NJ.MATH
122.
Zurück zum Zitat Leung YJ, Colton D (2012) Complex transmission eigenvalues for spherically stratified media. Inverse Problems 28:2944956.MathSciNet Leung YJ, Colton D (2012) Complex transmission eigenvalues for spherically stratified media. Inverse Problems 28:2944956.MathSciNet
123.
Zurück zum Zitat Levin B Y (1996) Lectures on Entire Functions. American Mathematical Society. Providence, RI.MATH Levin B Y (1996) Lectures on Entire Functions. American Mathematical Society. Providence, RI.MATH
124.
Zurück zum Zitat Lions J, Magenes E (1972) Non-homogeneous Boundary Value Problems and Applications. Springer, New York. Lions J, Magenes E (1972) Non-homogeneous Boundary Value Problems and Applications. Springer, New York.
125.
Zurück zum Zitat Magnus W (1949) Fragen der Eindeutigkeit und des Verhattens im Unendlichen für Lösungen von Δ u + k 2 u = 0. Abh. Math. Sem. Hamburg 16:77–94.MathSciNetMATH Magnus W (1949) Fragen der Eindeutigkeit und des Verhattens im Unendlichen für Lösungen von Δ u + k 2 u = 0. Abh. Math. Sem. Hamburg 16:77–94.MathSciNetMATH
126.
Zurück zum Zitat McLaughlin JR, Polyakov PL (1994) On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues. J. Differential Equations 107:351–382.MathSciNetMATH McLaughlin JR, Polyakov PL (1994) On the uniqueness of a spherically symmetric speed of sound from transmission eigenvalues. J. Differential Equations 107:351–382.MathSciNetMATH
127.
Zurück zum Zitat McLean W (2000) Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge.MATH McLean W (2000) Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge.MATH
128.
Zurück zum Zitat Mönch L (1997) On the inverse acoustic scattering problem by an open arc: the sound-hard case. Inverse Problems 13:1379–1392MathSciNetMATH Mönch L (1997) On the inverse acoustic scattering problem by an open arc: the sound-hard case. Inverse Problems 13:1379–1392MathSciNetMATH
129.
Zurück zum Zitat Monk P (2003) Finite Element Methods for Maxwell’s Equations. Oxford University Press, Oxford.MATH Monk P (2003) Finite Element Methods for Maxwell’s Equations. Oxford University Press, Oxford.MATH
130.
Zurück zum Zitat Morozov VA (1984) Methods for Solving Incorrectly Posed Problems. Springer, New York. Morozov VA (1984) Methods for Solving Incorrectly Posed Problems. Springer, New York.
131.
Zurück zum Zitat Müller C (1952) Über die ganzen Lösungen der Wellengleichung. Math. Annalen 124:235–264MATH Müller C (1952) Über die ganzen Lösungen der Wellengleichung. Math. Annalen 124:235–264MATH
132.
Zurück zum Zitat Nintcheu Fata S, Guzina BB (2004) A linear sampling method for near-field inverse problems in elastodynamics. Inverse Problems 20:713–736.MathSciNetMATH Nintcheu Fata S, Guzina BB (2004) A linear sampling method for near-field inverse problems in elastodynamics. Inverse Problems 20:713–736.MathSciNetMATH
133.
Zurück zum Zitat Norris AN (1998) A direct inverse scattering method for imaging obstacles with unknown surface conditions. IMA J. Applied Math. 61:267–290.MathSciNetMATH Norris AN (1998) A direct inverse scattering method for imaging obstacles with unknown surface conditions. IMA J. Applied Math. 61:267–290.MathSciNetMATH
134.
Zurück zum Zitat Päivärinta L, Sylvester J. (2008) Transmission eigenvalues. SIAM J. Math. Anal. 40 738–753. Päivärinta L, Sylvester J. (2008) Transmission eigenvalues. SIAM J. Math. Anal. 40 738–753.
135.
Zurück zum Zitat Pelekanos G, Sevroglou V (2003) Inverse scattering by penetrable objects in two-dimensional elastodynamics. J. Comp. Appl. Math. 151:129–140.MathSciNetMATH Pelekanos G, Sevroglou V (2003) Inverse scattering by penetrable objects in two-dimensional elastodynamics. J. Comp. Appl. Math. 151:129–140.MathSciNetMATH
136.
Zurück zum Zitat Piana M (1998) On uniqueness for anisotropic inhomogeneous inverse scattering problems. Inverse Problems 14:1565–1579.MathSciNetMATH Piana M (1998) On uniqueness for anisotropic inhomogeneous inverse scattering problems. Inverse Problems 14:1565–1579.MathSciNetMATH
137.
Zurück zum Zitat Potthast R (1999) Electromagnetic scattering from an orthotropic medium. J. Integral Equations Appl. 11:197–215.MathSciNetMATH Potthast R (1999) Electromagnetic scattering from an orthotropic medium. J. Integral Equations Appl. 11:197–215.MathSciNetMATH
138.
Zurück zum Zitat Potthast R (2000) Stability estimates and reconstructions in inverse acoustic scattering using singular sources. J. Comp. Appl. Math. 114:247–274.MathSciNetMATH Potthast R (2000) Stability estimates and reconstructions in inverse acoustic scattering using singular sources. J. Comp. Appl. Math. 114:247–274.MathSciNetMATH
139.
Zurück zum Zitat Potthast R (2001) Point Sourse and Multipoles in Inverse Scattering Theory. Research Notes in Mathematics, Vol 427, Chapman and Hall/CRC, Boca Raton, FL. Potthast R (2001) Point Sourse and Multipoles in Inverse Scattering Theory. Research Notes in Mathematics, Vol 427, Chapman and Hall/CRC, Boca Raton, FL.
140.
Zurück zum Zitat Potthast R (2004) A new non-iterative singular sources method for the reconstruction of piecewise constant media. Numer. Math. 98:703–730.MathSciNetMATH Potthast R (2004) A new non-iterative singular sources method for the reconstruction of piecewise constant media. Numer. Math. 98:703–730.MathSciNetMATH
141.
Zurück zum Zitat Potthast R, Sylvester J, Kusiak S (2003) A ’range test’ for determining scatterers with unknown physical properties. Inverse Problems 19:533–47.MathSciNetMATH Potthast R, Sylvester J, Kusiak S (2003) A ’range test’ for determining scatterers with unknown physical properties. Inverse Problems 19:533–47.MathSciNetMATH
142.
Zurück zum Zitat Pöschel J, Trubowitz E (1987) Inverse Spectral Theory. Academic, Boston.MATH Pöschel J, Trubowitz E (1987) Inverse Spectral Theory. Academic, Boston.MATH
143.
Zurück zum Zitat Rellich F (1943) Über das asymptotische Verhalten der Lösungen von △ u +λ u = 0 im unendlichen Gebieten. Jber. Deutsch. Math. Verein. 53:57–65.MathSciNetMATH Rellich F (1943) Über das asymptotische Verhalten der Lösungen von △ u +λ u = 0 im unendlichen Gebieten. Jber. Deutsch. Math. Verein. 53:57–65.MathSciNetMATH
144.
146.
Zurück zum Zitat Rondi L (2003) Unique determination of non-smooth sound-soft scatteres by finitely many far field measurements. Indiana University Math. J. 52:1631–62.MathSciNetMATH Rondi L (2003) Unique determination of non-smooth sound-soft scatteres by finitely many far field measurements. Indiana University Math. J. 52:1631–62.MathSciNetMATH
147.
Zurück zum Zitat Rundell W, Sacks P (1992) Reconstruction techniques for classical inverse Sturm-Liouville problems. Math. Comput. 58:161–183.MathSciNetMATH Rundell W, Sacks P (1992) Reconstruction techniques for classical inverse Sturm-Liouville problems. Math. Comput. 58:161–183.MathSciNetMATH
148.
Zurück zum Zitat Rynne BP, Sleeman BD (1991) The interior transmission problem and inverse scattering from inhomogeneous media. SIAM J. Math. Anal. 22:1755–1762.MathSciNetMATH Rynne BP, Sleeman BD (1991) The interior transmission problem and inverse scattering from inhomogeneous media. SIAM J. Math. Anal. 22:1755–1762.MathSciNetMATH
149.
Zurück zum Zitat Schechter M (2002) Principles of Functional Analysis, 2nd edn. American Mathematical Society, Providence, RI. Schechter M (2002) Principles of Functional Analysis, 2nd edn. American Mathematical Society, Providence, RI.
150.
Zurück zum Zitat Sevroglou V (2005) The far-field operator for penetrable and absorbing obstacles in 2D inverse elastic scattering. Inverse Problems 21:717–738.MathSciNetMATH Sevroglou V (2005) The far-field operator for penetrable and absorbing obstacles in 2D inverse elastic scattering. Inverse Problems 21:717–738.MathSciNetMATH
151.
Zurück zum Zitat Stefanov P, Uhlmann G (2004) Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering. Proc. Am. Math. Soc. 132:1351–54.MathSciNetMATH Stefanov P, Uhlmann G (2004) Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering. Proc. Am. Math. Soc. 132:1351–54.MathSciNetMATH
152.
Zurück zum Zitat Stephan EP (1987) Boundary integral equations for screen problems in ℝ 3. Integral Equations Operator Theory 10:236–257.MathSciNetMATH Stephan EP (1987) Boundary integral equations for screen problems in 3. Integral Equations Operator Theory 10:236–257.MathSciNetMATH
153.
Zurück zum Zitat Stephan EP, Wendland W (1984) An augmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems. Appl. Anal. 18:183–219.MathSciNet Stephan EP, Wendland W (1984) An augmented Galerkin procedure for the boundary integral method applied to two-dimensional screen and crack problems. Appl. Anal. 18:183–219.MathSciNet
154.
Zurück zum Zitat Sylvester J (2012) Discreteness of transmission eigenvalues via upper triangular compact operator. SIAM J. Math. Anal. 44:341–354.MathSciNetMATH Sylvester J (2012) Discreteness of transmission eigenvalues via upper triangular compact operator. SIAM J. Math. Anal. 44:341–354.MathSciNetMATH
155.
Zurück zum Zitat Tacchino A, Coyle J, Piana M (2002) Numerical validation of the linear sampling method. Inverse Problems 18:511–527.MathSciNetMATH Tacchino A, Coyle J, Piana M (2002) Numerical validation of the linear sampling method. Inverse Problems 18:511–527.MathSciNetMATH
156.
Zurück zum Zitat Ursell F (1978) On the exterior problems of acoustics II. Proc. Cambridge Phil. Soc. 84:545–548.MathSciNetMATH Ursell F (1978) On the exterior problems of acoustics II. Proc. Cambridge Phil. Soc. 84:545–548.MathSciNetMATH
157.
Zurück zum Zitat Vekua IN (1943) Metaharmonic functions. Trudy Tbilisskogo Matematichesgo Instituta 12:105–174. Vekua IN (1943) Metaharmonic functions. Trudy Tbilisskogo Matematichesgo Instituta 12:105–174.
158.
Zurück zum Zitat Xu Y, Mawata C, Lin W (2000) Generalized dual space indicator method for underwater imaging. Inverse Problems 16:1761–1776.MathSciNetMATH Xu Y, Mawata C, Lin W (2000) Generalized dual space indicator method for underwater imaging. Inverse Problems 16:1761–1776.MathSciNetMATH
159.
Zurück zum Zitat You YX, Miao GP (2002) An indicator sampling method for solving the inverse acoustic scattering problem from penetrable obstacles. Inverse Problems 18:859–880.MathSciNetMATH You YX, Miao GP (2002) An indicator sampling method for solving the inverse acoustic scattering problem from penetrable obstacles. Inverse Problems 18:859–880.MathSciNetMATH
160.
Zurück zum Zitat You YX, Miao GP, Liu YZ (2000) A fast method for acoustic imaging of multiple three-dimensional objects. J. Acoust. Soc. Am. 108:31–37. You YX, Miao GP, Liu YZ (2000) A fast method for acoustic imaging of multiple three-dimensional objects. J. Acoust. Soc. Am. 108:31–37.
161.
Zurück zum Zitat Young RM (2001) An Introduction to Nonharmonic Fourier Series. Academic, San Diego.MATH Young RM (2001) An Introduction to Nonharmonic Fourier Series. Academic, San Diego.MATH
Metadaten
Titel
Inverse Scattering Problems for Orthotropic Media
verfasst von
Fioralba Cakoni
David Colton
Copyright-Jahr
2014
Verlag
Springer US
DOI
https://doi.org/10.1007/978-1-4614-8827-9_6

Neuer Inhalt