Isoperimetric Inequalities for a Wedge-Like Membrane

Abdelhalim Hasnaoui; Lotfi Hermi

doi:10.1007/s00023-013-0243-y

Isoperimetric Inequalities for a Wedge-Like Membrane

Abdelhalim Hasnaoui
, Lotfi Hermi

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

For a wedge-like membrane, Payne and Weinberger proved in 1960 an isoperimetric inequality for the fundamental eigenvalue which in some cases improves the classical isoperimetric inequality of Faber-Krahn. In this work, we introduce "relative torsional rigidity" for this type of membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, Pólya-Szego{double acute}, Payne, Payne-Rayner, Chiti, and Talenti, which link the eigenvalue problem with the boundary value problem in a fundamental way.

Original language	English (US)
Pages (from-to)	369-406
Number of pages	38
Journal	Annales Henri Poincare
Volume	15
Issue number	2
DOIs	https://doi.org/10.1007/s00023-013-0243-y
State	Published - Feb 2014
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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10.1007/s00023-013-0243-y

Cite this

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title = "Isoperimetric Inequalities for a Wedge-Like Membrane",

abstract = "For a wedge-like membrane, Payne and Weinberger proved in 1960 an isoperimetric inequality for the fundamental eigenvalue which in some cases improves the classical isoperimetric inequality of Faber-Krahn. In this work, we introduce {"}relative torsional rigidity{"} for this type of membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, P{\'o}lya-Szego\{double acute\}, Payne, Payne-Rayner, Chiti, and Talenti, which link the eigenvalue problem with the boundary value problem in a fundamental way.",

author = "Abdelhalim Hasnaoui and Lotfi Hermi",

note = "Funding Information: This work was supported by travel funding from the University of Arizona and University of Tunis El Manar. We would like to thank Professors M. S. Ashbaugh, F. Chiacchio, L. Friedlander and N. Gamara for useful conversations and references. We are grateful to CIRM-Luminy, Marseille, for funding during the stay at the workshop “Shape Optimization Problems and Spectral Theory” (May 2012) where some of this work was completed.",

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doi = "10.1007/s00023-013-0243-y",

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AU - Hasnaoui, Abdelhalim

AU - Hermi, Lotfi

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PY - 2014/2

Y1 - 2014/2

N2 - For a wedge-like membrane, Payne and Weinberger proved in 1960 an isoperimetric inequality for the fundamental eigenvalue which in some cases improves the classical isoperimetric inequality of Faber-Krahn. In this work, we introduce "relative torsional rigidity" for this type of membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, Pólya-Szego{double acute}, Payne, Payne-Rayner, Chiti, and Talenti, which link the eigenvalue problem with the boundary value problem in a fundamental way.

AB - For a wedge-like membrane, Payne and Weinberger proved in 1960 an isoperimetric inequality for the fundamental eigenvalue which in some cases improves the classical isoperimetric inequality of Faber-Krahn. In this work, we introduce "relative torsional rigidity" for this type of membrane and prove new isoperimetric inequalities in the spirit of Saint-Venant, Pólya-Szego{double acute}, Payne, Payne-Rayner, Chiti, and Talenti, which link the eigenvalue problem with the boundary value problem in a fundamental way.

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DO - 10.1007/s00023-013-0243-y

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EP - 406

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 2

ER -

Isoperimetric Inequalities for a Wedge-Like Membrane

Abstract

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