A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918036687028224 |
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| author | Hatcher, Lawford |
| author_facet | Hatcher, Lawford |
| contents | We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two seemingly new estimates on the first mixed eigenvalue to give explicit examples of when the Dirichlet region is sufficiently small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03908 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region Hatcher, Lawford Analysis of PDEs Spectral Theory 35P05, 35B38, 35J05, 35J25, 58J50 We prove that on convex domains, first mixed Laplace eigenfunctions have no interior critical points if the Dirichlet region is connected and sufficiently small. We also find two seemingly new estimates on the first mixed eigenvalue to give explicit examples of when the Dirichlet region is sufficiently small. |
| title | A hot spots theorem for the mixed eigenvalue problem with small Dirichlet region |
| topic | Analysis of PDEs Spectral Theory 35P05, 35B38, 35J05, 35J25, 58J50 |
| url | https://arxiv.org/abs/2409.03908 |