Extremum problems of Laplacian eigenvalues and generalized Polya conjecture

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Abstract

In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl’s asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.

Original languageEnglish (US)
Pages (from-to)497-512
Number of pages16
JournalChinese Annals of Mathematics. Series B
Volume38
Issue number2
DOIs
StatePublished - Mar 1 2017

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Keywords

  • Extremum problems
  • Laplacian eigenvalues
  • Polya’s conjecture
  • Regularity of minimizers
  • Spliting equality
  • Weyl asymptotics

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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