The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909124805001216 |
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| author | Cai, Yingying Zhuge, Jinping |
| author_facet | Cai, Yingying Zhuge, Jinping |
| contents | Let $P$ be a bounded $n$-dimensional Lipschitz polytope, and let $φ_λ$ be a Dirichlet Laplace eigenfunction in $P$ corresponding to the eigenvalue $λ$. We show that the $(n-1)$-dimensional Hausdorff measure of the nodal set of $φ_λ$ does not exceed $C(P)\sqrtλ$. Our result extends the previous ones in quaisconvex domains (including $C^1$ and convex domains) to general polytopes that are not necessarily quasiconvex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes Cai, Yingying Zhuge, Jinping Analysis of PDEs 35A02, 35P05 Let $P$ be a bounded $n$-dimensional Lipschitz polytope, and let $φ_λ$ be a Dirichlet Laplace eigenfunction in $P$ corresponding to the eigenvalue $λ$. We show that the $(n-1)$-dimensional Hausdorff measure of the nodal set of $φ_λ$ does not exceed $C(P)\sqrtλ$. Our result extends the previous ones in quaisconvex domains (including $C^1$ and convex domains) to general polytopes that are not necessarily quasiconvex. |
| title | The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes |
| topic | Analysis of PDEs 35A02, 35P05 |
| url | https://arxiv.org/abs/2403.00279 |