JournalsjstVol. 6, No. 4pp. 735–745

On the number of Courant-sharp Dirichlet eigenvalues

  • Michiel van den Berg

    University of Bristol, UK

  • Katie Gittins

    University of Bristol, UK
On the number of Courant-sharp Dirichlet eigenvalues cover
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Abstract

We consider arbitrary open sets  in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of , (ii) the number of Courant-sharp Dirichlet eigenvalues of . This extends recent results of P. Bérard and B. Helffer.

Cite this article

Michiel van den Berg, Katie Gittins, On the number of Courant-sharp Dirichlet eigenvalues. J. Spectr. Theory 6 (2016), no. 4, pp. 735–745

DOI 10.4171/JST/139