On the second eigenvalue of the Laplacian in an annulus (Q938627)
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scientific article; zbMATH DE number 5316799
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the second eigenvalue of the Laplacian in an annulus |
scientific article; zbMATH DE number 5316799 |
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On the second eigenvalue of the Laplacian in an annulus (English)
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26 August 2008
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Motivated by a conjecture of Payne on nodal sets (the zeroes of the eigenfunctions of the Laplace operator), the author shows that the multiplicity of the second eigenvalue of both Dirichlet and Neumann Laplacians on an annulus is equal to \(n\), provided that the annulus is contained in one of the following \(n\) dimensional manifolds: the Euclidean space, a sphere or a hyperbolic space.
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eigenvalue multiplicity
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Dirichlet Laplacian
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Neumann Laplacian
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