On extending the inequalities of Payne, Pólya, and Weinberger using spherical harmonics

Mark S. Ashbaugh, Lotfi Hermi

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Using spherical harmonics, rearrangement techniques, the Sobolev inequality, and Chiti's reverse Hölder inequality, we obtain extensions of a classical result of Payne, Polya, and Weinberger bounding the gap between consecutive eigenvalues of the Dirichlet Laplacian in terms of moments of the preceding ones. The extensions yield domain-dependent inequalities.

Original languageEnglish (US)
Pages (from-to)1037-1072
Number of pages36
JournalRocky Mountain Journal of Mathematics
Volume38
Issue number4
DOIs
StatePublished - Sep 1 2008

Keywords

  • Dirichlet eigenvalue problem for domains in euclidean space
  • Domain-dependent inequalities for eigen-values
  • Eigenvalues ot the laplacian
  • H.C. Yang inequality
  • Hile-protter inequality
  • Payne-pólya-weinberger inequality

ASJC Scopus subject areas

  • Mathematics(all)

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