Skip to main content
Erschienen in: Journal of Inequalities and Applications 1/2010

Open Access 01.12.2010 | Research Article

Poincaré Inequalities with Luxemburg Norms in https://static-content.springer.com/image/art%3A10.1155%2F2010%2F241759/MediaObjects/13660_2009_Article_2092_IEq1_HTML.gif -Averaging Domains

verfasst von: Yuming Xing

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2010

Einloggen

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

search-config
loading …

Abstract

We prove both local and global Poincaré inequalities with Luxemburg norms for differential forms in https://static-content.springer.com/image/art%3A10.1155%2F2010%2F241759/MediaObjects/13660_2009_Article_2092_IEq2_HTML.gif -averaging domains, which can be considered as generalizations of the existing versions of Poincaré inequalities.

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 "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!

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!

Literatur
[1]
Zurück zum Zitat Staples SG: -averaging domains and the Poincaré inequality. Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1989, 14(1):103–127.MATHMathSciNetCrossRef Staples SG: https://static-content.springer.com/image/art%3A10.1155%2F2010%2F241759/MediaObjects/13660_2009_Article_2092_IEq327_HTML.gif -averaging domains and the Poincaré inequality. Annales Academiae Scientiarum Fennicae. Series A I. Mathematica 1989, 14(1):103–127.MATHMathSciNetCrossRef
[2]
Zurück zum Zitat Ding S, Nolder CA: Weighted Poincaré inequalities for solutions to -harmonic equations. Illinois Journal of Mathematics 2002, 46(1):199–205.MATHMathSciNet Ding S, Nolder CA: Weighted Poincaré inequalities for solutions to -harmonic equations. Illinois Journal of Mathematics 2002, 46(1):199–205.MATHMathSciNet
[3]
Zurück zum Zitat Wang Y: Two-weight Poincaré-type inequalities for differential forms in -averaging domains. Applied Mathematics Letters 2007, 20(11):1161–1166. 10.1016/j.aml.2007.02.003MATHMathSciNetCrossRef Wang Y: Two-weight Poincaré-type inequalities for differential forms in -averaging domains. Applied Mathematics Letters 2007, 20(11):1161–1166. 10.1016/j.aml.2007.02.003MATHMathSciNetCrossRef
[4]
Zurück zum Zitat Wang Y, Wu C: Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous -harmonic equation. Computers and Mathematics with Applications 2004, 47(10–11):1545–1554. 10.1016/j.camwa.2004.06.006MATHMathSciNetCrossRef Wang Y, Wu C: Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous -harmonic equation. Computers and Mathematics with Applications 2004, 47(10–11):1545–1554. 10.1016/j.camwa.2004.06.006MATHMathSciNetCrossRef
[5]
Zurück zum Zitat Xing Y: Weighted Poincaré-type estimates for conjugate -harmonic tensors. Journal of Inequalities and Applications 2005, (1):1–6. Xing Y: Weighted Poincaré-type estimates for conjugate -harmonic tensors. Journal of Inequalities and Applications 2005, (1):1–6.
[6]
Zurück zum Zitat Liu B: -weighted imbedding inequalities for -harmonic tensors. Journal of Mathematical Analysis and Applications 2002, 273(2):667–676. 10.1016/S0022-247X(02)00331-1MATHMathSciNetCrossRef Liu B: https://static-content.springer.com/image/art%3A10.1155%2F2010%2F241759/MediaObjects/13660_2009_Article_2092_IEq332_HTML.gif -weighted imbedding inequalities for -harmonic tensors. Journal of Mathematical Analysis and Applications 2002, 273(2):667–676. 10.1016/S0022-247X(02)00331-1MATHMathSciNetCrossRef
[7]
Zurück zum Zitat Xing Y, Ding S: Poincaré inequalities with the Radon measure for differential forms. Computers and Mathematics with Applications, Accepted Computers and Mathematics with Applications, Accepted Xing Y, Ding S: Poincaré inequalities with the Radon measure for differential forms. Computers and Mathematics with Applications, Accepted Computers and Mathematics with Applications, Accepted
[8]
Zurück zum Zitat Nolder CA: Hardy-Littlewood theorems for -harmonic tensors. Illinois Journal of Mathematics 1999, 43(4):613–632.MATHMathSciNet Nolder CA: Hardy-Littlewood theorems for -harmonic tensors. Illinois Journal of Mathematics 1999, 43(4):613–632.MATHMathSciNet
[9]
Zurück zum Zitat Ding S: Two-weight Caccioppoli inequalities for solutions of nonhomogeneous -harmonic equations on Riemannian manifolds. Proceedings of the American Mathematical Society 2004, 132(8):2367–2375. 10.1090/S0002-9939-04-07347-2MATHMathSciNetCrossRef Ding S: Two-weight Caccioppoli inequalities for solutions of nonhomogeneous -harmonic equations on Riemannian manifolds. Proceedings of the American Mathematical Society 2004, 132(8):2367–2375. 10.1090/S0002-9939-04-07347-2MATHMathSciNetCrossRef
[10]
Zurück zum Zitat Agarwal RP, O'Regan D, Shakhmurov VB: Separable anisotropic differential operators in weighted abstract spaces and applications. Journal of Mathematical Analysis and Applications 2008, 338(2):970–983. 10.1016/j.jmaa.2007.05.078MATHMathSciNetCrossRef Agarwal RP, O'Regan D, Shakhmurov VB: Separable anisotropic differential operators in weighted abstract spaces and applications. Journal of Mathematical Analysis and Applications 2008, 338(2):970–983. 10.1016/j.jmaa.2007.05.078MATHMathSciNetCrossRef
[11]
Zurück zum Zitat Agarwal RP, Diagana T, Hernández EM: Weighted pseudo almost periodic solutions to some partial neutral functional differential equations. Journal of Nonlinear and Convex Analysis 2007, 8(3):397–415.MATHMathSciNet Agarwal RP, Diagana T, Hernández EM: Weighted pseudo almost periodic solutions to some partial neutral functional differential equations. Journal of Nonlinear and Convex Analysis 2007, 8(3):397–415.MATHMathSciNet
[12]
Zurück zum Zitat Yuming X: Weighted integral inequalities for solutions of the -harmonic equation. Journal of Mathematical Analysis and Applications 2003, 279(1):350–363. 10.1016/S0022-247X(03)00036-2MATHMathSciNetCrossRef Yuming X: Weighted integral inequalities for solutions of the -harmonic equation. Journal of Mathematical Analysis and Applications 2003, 279(1):350–363. 10.1016/S0022-247X(03)00036-2MATHMathSciNetCrossRef
[13]
Zurück zum Zitat Buckley SM, Koskela P: Orlicz-Hardy inequalities. Illinois Journal of Mathematics 2004, 48(3):787–802.MATHMathSciNet Buckley SM, Koskela P: Orlicz-Hardy inequalities. Illinois Journal of Mathematics 2004, 48(3):787–802.MATHMathSciNet
[14]
Zurück zum Zitat Ding S: -averaging domains and the quasi-hyperbolic metric. Computers & Mathematics with Applications 2004, 47(10–11):1611–1618. 10.1016/j.camwa.2004.06.016MATHMathSciNetCrossRef Ding S: https://static-content.springer.com/image/art%3A10.1155%2F2010%2F241759/MediaObjects/13660_2009_Article_2092_IEq337_HTML.gif -averaging domains and the quasi-hyperbolic metric. Computers & Mathematics with Applications 2004, 47(10–11):1611–1618. 10.1016/j.camwa.2004.06.016MATHMathSciNetCrossRef
[15]
Zurück zum Zitat Ding S, Nolder CA: -averaging domains. Journal of Mathematical Analysis and Applications 2003, 283(1):85–99. 10.1016/S0022-247X(03)00216-6MATHMathSciNetCrossRef Ding S, Nolder CA: https://static-content.springer.com/image/art%3A10.1155%2F2010%2F241759/MediaObjects/13660_2009_Article_2092_IEq338_HTML.gif -averaging domains. Journal of Mathematical Analysis and Applications 2003, 283(1):85–99. 10.1016/S0022-247X(03)00216-6MATHMathSciNetCrossRef
[16]
Zurück zum Zitat Agarwal RP, Ding S, Nolder CA: Inequalities for Differential Forms. Springer, New York, NY, USA; 2009:xvi+387.MATHCrossRef Agarwal RP, Ding S, Nolder CA: Inequalities for Differential Forms. Springer, New York, NY, USA; 2009:xvi+387.MATHCrossRef
[17]
Zurück zum Zitat Staples SG: Averaging domains: from Euclidean spaces to homogeneous spaces. In Differential & Difference Equations and Applications. Hindawi, New York, NY, USA; 2006:1041–1048. Staples SG: Averaging domains: from Euclidean spaces to homogeneous spaces. In Differential & Difference Equations and Applications. Hindawi, New York, NY, USA; 2006:1041–1048.
[18]
Zurück zum Zitat Stein EM: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series. Volume 43. Princeton University Press, Princeton, NJ, USA; 1993:xiv+695. Stein EM: Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series. Volume 43. Princeton University Press, Princeton, NJ, USA; 1993:xiv+695.
Metadaten
Titel
Poincaré Inequalities with Luxemburg Norms in -Averaging Domains
verfasst von
Yuming Xing
Publikationsdatum
01.12.2010
Verlag
Springer International Publishing
Erschienen in
Journal of Inequalities and Applications / Ausgabe 1/2010
Elektronische ISSN: 1029-242X
DOI
https://doi.org/10.1155/2010/241759

Weitere Artikel der Ausgabe 1/2010

Journal of Inequalities and Applications 1/2010 Zur Ausgabe

Premium Partner