TY - JOUR
T1 - Isoperimetric Inequalities for a Wedge-Like Membrane
AU - Hasnaoui, Abdelhalim
AU - Hermi, Lotfi
N1 - 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.
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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U2 - 10.1007/s00023-013-0243-y
DO - 10.1007/s00023-013-0243-y
M3 - Article
AN - SCOPUS:84895911209
VL - 15
SP - 369
EP - 406
JO - Annales Henri Poincare
JF - Annales Henri Poincare
SN - 1424-0637
IS - 2
ER -