References
S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. Pure. Appl. Math.12 (1959), 623–727.
C. A. Berenstein,On the converse to Pompeiu’s problem, Notas e CommunicacŌes de Mathemática, Univ. Fed. de Pernarabuco,73, 1976.
L. Brown, B. M. Schreiber, and B. A. Taylor,Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier23 (1973), 125–154.
N. de Bruijn,Asymptotic Methods in Analysis, North-Holland, 1961.
L. A. Cafarelli,The regularity of free boundaries in higher dimensions, Acta Math.139 (1977), 155–184.
R. Courant and D. Hilbert,Methods of Mathematical Physics, Interscience, 1953.
C. Dafermos,Contraction Semigroups and Trend to Equilibrium in Continuum Mechanics, Springer Lecture Notes in Mathematics503 (1976), 295–306.
L. Ehrenpreis,Fourier Analysis in Several Complex Variables, Interscience, 1970.
D. Kinderlehrer and L. Nirenberg,Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa4 (1977), 373–391.
P. Nowosad, Operadores positivos e optimizacāo; aplicacŌes à energia nuclear, preprint, 1977.
R. Osserman,The isoperimetric inequality, Bull. Amer. Math. Soc.84 (1974), 1182–1238.
L. E. Payne,Inequalities for eigenvalues of membranes and plates, J. Rat. Mech. Analysis4 (1955), 517–529.
L. E. Payne,Isoperimetric inequalities and their applications, SIAM Rev.9 (1967), 413–488.
Lord Rayleigh,The Theory of Sound, MacMillan, 1877.
F. Rellich,Darstellung der Eigenwerte δu + λu durch ein Randintegral, Math. Z.46 (1940), 635–646.
J. Serrin,A symmetry problem in potential theory, Arch. Rational Mech. Anal.43 (1971), 304–318.
L. A. Shepp and J. B. Kruskal,Computerized tomography: the new medical X-ray technology, Amer. Math. Monthly85 (1978), 420–439.
K. T. Smith, D. C. Solmon and S. L. Wagner,Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math. Soc.83 (1977), 1227–1270.
R. Temam,A non-linear eigenvalue problem: The shape at equilibrium of a confined plasma. Arch. Rational Mech. Anal.60 (1975), 51–73.
H. F. Weinberger,Remark on the preceding paper of Serrin, Arch. Rational Mech. Anal.43 (1971), 319–320.
S. A. Williams,A partial solution of the Pompeiu problem, Math. Ann.223 (1976), 183–190.
L. Zalcman,Analyticity and the Pompeiu problem, Arch. Rational Mech. Anal.47 (1972), 237–254.
L. Zalcman,Offbeat integral geometry, preprint, 1978.
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Partially supported by NSF grant MCS 78-00811.
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Berenstein, C.A. An inverse spectral theorem and its relation to the Pompeiu problem. J. Anal. Math. 37, 128–144 (1980). https://doi.org/10.1007/BF02797683
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DOI: https://doi.org/10.1007/BF02797683