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 | |
| State | Published - Feb 2014 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
Cite this
Isoperimetric Inequalities for a Wedge-Like Membrane. / Hasnaoui, Abdelhalim; Hermi, Lotfi.
In: Annales Henri Poincare, Vol. 15, No. 2, 02.2014, p. 369-406.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Isoperimetric Inequalities for a Wedge-Like Membrane
AU - Hasnaoui, Abdelhalim
AU - Hermi, Lotfi
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.
UR - http://www.scopus.com/inward/record.url?scp=84895911209&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84895911209&partnerID=8YFLogxK
U2 - 10.1007/s00023-013-0243-y
DO - 10.1007/s00023-013-0243-y
M3 - Article
VL - 15
SP - 369
EP - 406
JO - Annales Henri Poincare
JF - Annales Henri Poincare
SN - 1424-0637
IS - 2
ER -