On the optimization of the Robin eigenvalues in some classes of polygons
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915505780031488 |
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| author | Carbotti, Alessandro Cito, Simone Pallara, Diego |
| author_facet | Carbotti, Alessandro Cito, Simone Pallara, Diego |
| contents | Given the eigenvalue problem for the Laplacian with Robin boundary conditions, (with $β\in\R\setminus\{0\}$ the Robin parameter), we consider a shape minimization problem for a function of the first eigenvalues if $β>0$ and a shape maximization problem if $β<0$. Both problems are settled in a suitable class of generalized polygons with an upper bound on the number of sides, under either perimeter or volume constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03502 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the optimization of the Robin eigenvalues in some classes of polygons Carbotti, Alessandro Cito, Simone Pallara, Diego Analysis of PDEs (Primary) 49Q10, (Secondary) 35P15, 49R05 Given the eigenvalue problem for the Laplacian with Robin boundary conditions, (with $β\in\R\setminus\{0\}$ the Robin parameter), we consider a shape minimization problem for a function of the first eigenvalues if $β>0$ and a shape maximization problem if $β<0$. Both problems are settled in a suitable class of generalized polygons with an upper bound on the number of sides, under either perimeter or volume constraint. |
| title | On the optimization of the Robin eigenvalues in some classes of polygons |
| topic | Analysis of PDEs (Primary) 49Q10, (Secondary) 35P15, 49R05 |
| url | https://arxiv.org/abs/2508.03502 |