A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains

Abdelhalim Hasnaoui, Lotfi Hermi

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

By introducing new geometric factors which lend themselves to the Payne interpretation in Weinstein fractional space, we prove new isoperimetric inequalities which complement those of Payne–Weinberger and Saint-Venant giving a new upper bound for the fundamental mode of vibration of a wedge-like membrane and a new lower bound for its “relative torsional rigidity”. We also prove a new weighted version of a result of Crooke–Sperb for the associated fundamental eigenfunction of the Dirichlet Laplacian for such domains. A new weighted Rellich-type identity for wedge-like domains is also proved to achieve this latter task.

Original languageEnglish (US)
Pages (from-to)2419-2440
Number of pages22
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume66
Issue number5
DOIs
StatePublished - Apr 29 2015

Keywords

  • Crooke–Sperb inequality
  • Fundamental eigenvalue
  • Isoperimetric Saint-Venant inequality
  • Upper bound
  • Wedge-like membrane

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Physics and Astronomy(all)

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