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arXiv · 1903.05998

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

Bernard Helffer·Thomas Hoffmann-Ostenhof·François Jauberteau·Corentin Léna
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Abstract

We revisit an interesting example proposed by Maria Hoffmann-Ostenhof, the second author and Nikolai Nadirashvili of a bounded domain in R2 for which the second eigenvalue of the Dirichlet Laplacian has multiplicity three. 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.

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Bernard Helffer, Thomas Hoffmann-Ostenhof, François Jauberteau, Corentin Léna. 2019-03-14. On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains--with some numerics--. https://arxiv.org/abs/1903.05998

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