Talenti comparison results for solutions to $p$-Laplace equation on multiply connected domains
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912825802227712 |
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| author | Barbato, Luca Salerno, Francesco |
| author_facet | Barbato, Luca Salerno, Francesco |
| contents | In the last years comparison results of Talenti type for Elliptic Problems have been widely investigated. In this paper we obtain a comparison result for the $p$-Laplace operator in multiply connected domains with Robin boundary condition on the exterior boundary and non-homogeneous Dirichlet boundary conditions on the interior one, generalizing the results obtained in \cite{ANT, AGM} to this type of domains. This will be a generalization to Robin boundary condition of the results obtained in \cite{B, B2}, with an improvement of the $L^2$ comparison in the case $p=2$. As a consequence, we obtain a Bossel-Daners and Saint-Venant type inequalities for multiply connected domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Talenti comparison results for solutions to $p$-Laplace equation on multiply connected domains Barbato, Luca Salerno, Francesco Analysis of PDEs 35J92, 35B51, 35P30 In the last years comparison results of Talenti type for Elliptic Problems have been widely investigated. In this paper we obtain a comparison result for the $p$-Laplace operator in multiply connected domains with Robin boundary condition on the exterior boundary and non-homogeneous Dirichlet boundary conditions on the interior one, generalizing the results obtained in \cite{ANT, AGM} to this type of domains. This will be a generalization to Robin boundary condition of the results obtained in \cite{B, B2}, with an improvement of the $L^2$ comparison in the case $p=2$. As a consequence, we obtain a Bossel-Daners and Saint-Venant type inequalities for multiply connected domains. |
| title | Talenti comparison results for solutions to $p$-Laplace equation on multiply connected domains |
| topic | Analysis of PDEs 35J92, 35B51, 35P30 |
| url | https://arxiv.org/abs/2504.06103 |