On the number of Courant-sharp Dirichlet eigenvalues

DOI10.4171/JST/139zbMath1372.35197arXiv1602.08376MaRDI QIDQ516569

Katie Gittins, Michiel van den Berg

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/1602.08376

zbMATH Keywords

Weyl's theoremDirichlet Laplaciannodal domainsPleijel's theorem

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Variational methods for eigenvalues of operators (49R05)

Related Items (3)

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

Cites Work

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• The weak Pleijel theorem with geometric control
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• Heat equation on the arithmetic von Koch snowflake
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• On the heat content of a polygon
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• 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
• On Pleijel's Nodal Domain Theorem
• Fourier Tauberian theorems and applications

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