A quantitative Talenti-type comparison result 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_ | 1866915618582691840 |
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| author | Amato, Vincenzo Barbato, Rosa Cito, Simone Masiello, Alba Lia Paoli, Gloria |
| author_facet | Amato, Vincenzo Barbato, Rosa Cito, Simone Masiello, Alba Lia Paoli, Gloria |
| contents | The purpose of this paper is to establish a quantitative version of the Talenti comparison principle for solutions to the Poisson equation with Robin boundary conditions. This quantitative enhancement is proved in terms of the asymmetry of domain. The key role is played by a careful analysis of the propagation of asymmetry for the level sets of the solutions of a PDE. As a byproduct, we obtain an alternative proof of the quantitative Saint-Venant inequality for the Robin torsion and, in the planar case, of the quantitative Faber-Krahn inequality for the first Robin eigenvalue. In addition, we complete the framework of the rigidity result of the Talenti inequalities with Robin boundary conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A quantitative Talenti-type comparison result with Robin boundary conditions Amato, Vincenzo Barbato, Rosa Cito, Simone Masiello, Alba Lia Paoli, Gloria Analysis of PDEs 35J05, 35J25, 35B35 The purpose of this paper is to establish a quantitative version of the Talenti comparison principle for solutions to the Poisson equation with Robin boundary conditions. This quantitative enhancement is proved in terms of the asymmetry of domain. The key role is played by a careful analysis of the propagation of asymmetry for the level sets of the solutions of a PDE. As a byproduct, we obtain an alternative proof of the quantitative Saint-Venant inequality for the Robin torsion and, in the planar case, of the quantitative Faber-Krahn inequality for the first Robin eigenvalue. In addition, we complete the framework of the rigidity result of the Talenti inequalities with Robin boundary conditions. |
| title | A quantitative Talenti-type comparison result with Robin boundary conditions |
| topic | Analysis of PDEs 35J05, 35J25, 35B35 |
| url | https://arxiv.org/abs/2511.11316 |