On the number of Courant-sharp Dirichlet eigenvalues

Michiel van den Berg, Katie Gittins

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
287 Downloads (Pure)

Abstract

We consider arbitrary open sets Ω in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of Ω, (ii) the number of Courant-sharp Dirichlet eigenvalues of Ω. This extends recent results of P. Bérard and B. Helffer.
Original languageEnglish
Pages (from-to)735-745
Number of pages11
JournalJournal of Spectral Theory
Volume6
Issue number4
DOIs
Publication statusPublished - 9 Dec 2016

Keywords

  • Weyl's theorem
  • Pleijel's theorem
  • Dirichlet Laplacian
  • Nodal domain

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