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

Mathematics

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

2 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 1 2014

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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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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