Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913685388132352 |
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| author | Pushnitski, Alexander Wigman, Igor |
| author_facet | Pushnitski, Alexander Wigman, Igor |
| contents | We study the eigenvalue clusters of the Robin Laplacian on the 2-dimensional hemisphere with a variable Robin coefficient on the equator. The $\ell$'th cluster has $\ell+1$ eigenvalues. We determine the asymptotic density of eigenvalues in the $\ell$'th cluster as $\ell$ tends to infinity. This density is given by an explicit integral involving the even part of the Robin coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07044 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition Pushnitski, Alexander Wigman, Igor Spectral Theory 35G15 We study the eigenvalue clusters of the Robin Laplacian on the 2-dimensional hemisphere with a variable Robin coefficient on the equator. The $\ell$'th cluster has $\ell+1$ eigenvalues. We determine the asymptotic density of eigenvalues in the $\ell$'th cluster as $\ell$ tends to infinity. This density is given by an explicit integral involving the even part of the Robin coefficient. |
| title | Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition |
| topic | Spectral Theory 35G15 |
| url | https://arxiv.org/abs/2309.07044 |