The weak Pleijel theorem with geometric control

DOI10.4171/JST/138zbMath1372.35194arXiv1512.07089MaRDI QIDQ516567

Bernard Helffer, Pierre H. Bérard

Publication date: 14 March 2017

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.07089

zbMATH Keywords

Dirichlet Laplaciannodal domainsCourant theoremPleijel theorem

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (4)

Courant-sharp eigenvalues of Neumann 2-rep-tiles ⋮ Pleijel's nodal domain theorem for Neumann and Robin eigenfunctions ⋮ Upper bounds for Courant-sharp Neumann and Robin eigenvalues ⋮ On the number of Courant-sharp Dirichlet eigenvalues

Cites Work

• Unnamed Item
• Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle
• Asymptotics for the spectrum of the Dirichlet laplacian on horn-shaped regions
• A general comparison theorem with applications to volume estimates for submanifolds
• A generalization of Courant's nodal domain theorem.
• Dirichlet Eigenfunctions of the Square Membrane: Courant’s Property, and A. Stern’s and Å. Pleijel’s Analyses
• Pleijel’s nodal domain theorem for free membranes
• Estimates for the Counting Function of the Laplace Operator on Domains with Rough Boundaries
• Dirichlet eigenfunctions on the cube, sharpening the Courant nodal inequality
• Fourier Tauberian theorems and applications

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