Isoperimetric Inequalities for a Wedge-Like Membrane

Abdelhalim Hasnaoui, Lotfi Hermi

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)369-406
Number of pages38
JournalAnnales Henri Poincare
Volume15
Issue number2
DOIs
StatePublished - Feb 2014

Fingerprint

Isoperimetric Inequality
Wedge
wedges
Membrane
membranes
eigenvalues
rigidity
boundary value problems
Acute
Rigidity
Eigenvalue Problem
Boundary Value Problem
Eigenvalue

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 journalArticle

Hasnaoui, Abdelhalim ; Hermi, Lotfi. / Isoperimetric Inequalities for a Wedge-Like Membrane. In: Annales Henri Poincare. 2014 ; Vol. 15, No. 2. pp. 369-406.
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