On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains – with some numerics

On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains – with some numerics –

Published:2020-12-02 Issue:1 Volume:121 Page:35-57
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Helffer B.¹²,Hoffmann-Ostenhof T.³,Jauberteau F.¹,Léna C.⁴

Affiliation:

1. Laboratoire de Mathématique Jean Leray, Université de Nantes, France

2. Laboratoire de Mathématiques d’Orsay, Unversité Paris Sud, France

3. Institut für Theoretische Chemie, University of Wien, Austria

4. Department of Mathematics, University of Stockholm, Sweden

Abstract

We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R 2 for which the second eigenvalue of the Dirichlet Laplacian has multiplicity 3. We also analyze carefully the first eigenvalues of the Laplacian in the case of the disk with two symmetric cracks placed on a smaller concentric disk in function of their size.

Publisher

IOS Press

Subject

General Mathematics

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