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Journal of Inequalities and Applications
Published in: Journal of Inequalities and Applications 1/2006

Open Access 01-12-2006 | Research Article

Applications of the poincaré inequality to extended Kantorovich method

Authors: Der-Chen Chang, Tristan Nguyen, Gang Wang, Norman M. Wereley

Published in: Journal of Inequalities and Applications | Issue 1/2006

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Abstract

We apply the Poincaré inequality to study the extended Kantorovich method that was used to construct a closed-form solution for two coupled partial differential equations with mixed boundary conditions.
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Literature
1.
Chang D-C, Wang G, Wereley NM: A generalized Kantorovich method and its application to free in-plane plate vibration problem. Applicable Analysis 2001,80(3–4):493–523.MathSciNetMATH
2.
Chang D-C, Wang G, Wereley NM: Analysis and applications of extended Kantorovich-Krylov method. Applicable Analysis 2003,82(7):713–740. 10.1080/0003681031000148573MathSciNetCrossRefMATH
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Evans LC: Partial Differential Equations, Graduate Studies in Mathematics. Volume 19. American Mathematical Society, Rhode Island; 1998:xviii+662.
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Farag NH, Pan J: Model characteristics of in-plane vibration of rectangular plates. Journal of Acoustics Society of America 1999,105(6):3295–3310. 10.1121/1.424658CrossRef
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John F: Partial Differential Equations, Applied Mathematical Sciences. Volume 1. 3rd edition. Springer, New York; 1978:ix+198.
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Kantorovich LV, Krylov VI: Approximate Method of Higher Analysis. Noordhoff, Groningen; 1964.
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Kerr AD: An extension of the Kantorovich method. Quarterly of Applied Mathematics 1968,26(2):219–229.MathSciNetMATH
8.
Kerr AD, Alexander H: An application of the extended Kantorovich method to the stress analysis of a clamped rectangular plate. Acta Mechanica 1968, 6: 180–196. 10.1007/BF01170382CrossRefMATH
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Lieb EH, Loss M: Analysis, Graduate Studies in Mathematics. Volume 14. American Mathematical Society, Rhode Island; 1997:xviii+278.
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Stein EM: Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, no. 30. Princeton University Press, New Jersey; 1970:xiv+290.
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Wang G, Wereley NM, Chang D-C: Analysis of sandwich plates with viscoelastic damping using two-dimensional plate modes. AIAA Journal 2003,41(5):924–932. 10.2514/2.2028CrossRef
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Wang G, Wereley NM, Chang D-C: Analysis of bending vibration of rectangular plates Using two-dimensional plate modes. AIAA Journal of Aircraft 2005,42(2):542–550. 10.2514/1.4303CrossRef
Metadata
Title
Applications of the poincaré inequality to extended Kantorovich method
Authors
Der-Chen Chang
Tristan Nguyen
Gang Wang
Norman M. Wereley
Publication date
01-12-2006
Publisher
Springer International Publishing
Published in
Journal of Inequalities and Applications / Issue 1/2006
Electronic ISSN: 1029-242X
DOI
https://doi.org/10.1155/JIA/2006/32356

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