Relations between principal eigenvalue and torsional rigidity with Robin boundary conditions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908717596803072 |
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| author | Buttazzo, Giuseppe Cito, Simone Solombrino, Francesco |
| author_facet | Buttazzo, Giuseppe Cito, Simone Solombrino, Francesco |
| contents | We consider the torsional rigidity and the principal eigenvalue related to the Laplace operator with Dirichlet and Robin boundary conditions. The goal is to find upper and lower bounds to products of suitable powers of the quantities above in the class of Lipschitz domains. The threshold exponent for the Robin case is explicitly recovered and shown to be strictly smaller than in the Dirichlet one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14927 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relations between principal eigenvalue and torsional rigidity with Robin boundary conditions Buttazzo, Giuseppe Cito, Simone Solombrino, Francesco Analysis of PDEs 49Q10, 49J45, 49R05, 35P15, 35J25 We consider the torsional rigidity and the principal eigenvalue related to the Laplace operator with Dirichlet and Robin boundary conditions. The goal is to find upper and lower bounds to products of suitable powers of the quantities above in the class of Lipschitz domains. The threshold exponent for the Robin case is explicitly recovered and shown to be strictly smaller than in the Dirichlet one. |
| title | Relations between principal eigenvalue and torsional rigidity with Robin boundary conditions |
| topic | Analysis of PDEs 49Q10, 49J45, 49R05, 35P15, 35J25 |
| url | https://arxiv.org/abs/2512.14927 |