On the number of Courant-sharp Dirichlet eigenvalues

Michiel van den Berg; Katie Gittins

doi:10.4171/JST/139

On the number of Courant-sharp Dirichlet eigenvalues

Michiel van den Berg, Katie Gittins

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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 language	English
Pages (from-to)	735-745
Number of pages	11
Journal	Journal of Spectral Theory
Volume	6
Issue number	4
DOIs	https://doi.org/10.4171/JST/139
Publication status	Published - 9 Dec 2016

Keywords

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

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10.4171/JST/139

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via European Mathematical Society at DOI: 10.4171/JST/139. Please refer to any applicable terms of use of the publisher.
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Professor Michiel van den Berg
- M.vandenBergbristol.acuk
- School of Mathematics - Emeritus Professor
- Probability, Analysis and Dynamics
- Pure Mathematics
- Analysis
Person: Member, Honorary and Visiting Academic

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title = "On the number of Courant-sharp Dirichlet eigenvalues",

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. B{\'e}rard and B. Helffer.",

keywords = "Weyl's theorem, Pleijel's theorem, Dirichlet Laplacian, Nodal domain",

author = "{van den Berg}, Michiel and Katie Gittins",

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AU - Gittins, Katie

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AB - 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.

KW - Weyl's theorem

KW - Pleijel's theorem

KW - Dirichlet Laplacian

KW - Nodal domain

U2 - 10.4171/JST/139

DO - 10.4171/JST/139

M3 - Article (Academic Journal)

SN - 1664-039X

VL - 6

SP - 735

EP - 745

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 4

ER -

On the number of Courant-sharp Dirichlet eigenvalues

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Keywords

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Professor Michiel van den Berg

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