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) |
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Pages (from-to) | 369-406 |
Number of pages | 38 |
Journal | Annales Henri Poincare |
Volume | 15 |
Issue number | 2 |
DOIs | |
State | Published - Feb 1 2014 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics