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

We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in [Formula: see text] for which the second eigenvalue of the Dirichlet Laplacian has multiplicity 3. We also analyze carefully the first eigenvalues of the Laplacian...

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Bibliographic Details
Published in:Asymptotic analysis 2021, Vol.121 (1), p.35-57
Main Authors: Helffer, B., Hoffmann-Ostenhof, T., Jauberteau, F., Léna, C.
Format: Article
Language:English
Subjects:
Cracks
Dirichlet problem
Domains
Eigenvalues
Laplacian
matematik
Mathematics
multiplicity
Spectral theory
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Summary:We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in [Formula: see text] 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.
ISSN:0921-7134
1875-8576
1875-8576
DOI:10.3233/ASY-191594