A note on the maximization of the first Dirichlet eigenvalue for perforated planar domains
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914854408814592 |
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| author | Dias, Manuel |
| author_facet | Dias, Manuel |
| contents | In this work we prove that given an open bounded set $Ω\subset \mathbb{R}^2$ with a $C^2$ boundary, there exists $ε:= ε(Ω)$ small enough such that for all $0 < δ< ε$ the maximum of $\{λ_1(Ω- B_δ(x)):B_δ \subset Ω\}$ is never attained when the ball is close enough to the boundary. In particular it is not obtained when $B_δ(x)$ is touching the boundary $\partial Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the maximization of the first Dirichlet eigenvalue for perforated planar domains Dias, Manuel Analysis of PDEs Optimization and Control Spectral Theory 35J25, 49R05, 49Q10, 35B65, 47J10 In this work we prove that given an open bounded set $Ω\subset \mathbb{R}^2$ with a $C^2$ boundary, there exists $ε:= ε(Ω)$ small enough such that for all $0 < δ< ε$ the maximum of $\{λ_1(Ω- B_δ(x)):B_δ \subset Ω\}$ is never attained when the ball is close enough to the boundary. In particular it is not obtained when $B_δ(x)$ is touching the boundary $\partial Ω$. |
| title | A note on the maximization of the first Dirichlet eigenvalue for perforated planar domains |
| topic | Analysis of PDEs Optimization and Control Spectral Theory 35J25, 49R05, 49Q10, 35B65, 47J10 |
| url | https://arxiv.org/abs/2407.01237 |