English

On the number of Courant-sharp Dirichlet eigenvalues

Spectral Theory 2017-03-31 v3 Analysis of PDEs

Abstract

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

Keywords

Cite

@article{arxiv.1602.08376,
  title  = {On the number of Courant-sharp Dirichlet eigenvalues},
  author = {Michiel van den Berg and Katie Gittins},
  journal= {arXiv preprint arXiv:1602.08376},
  year   = {2017}
}

Comments

10 pages, 2 figures

R2 v1 2026-06-22T12:58:42.339Z