A Talenti comparison result for a class of Neumann boundary value problems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914967548067840 |
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| author | Celentano, Antonio Nitsch, Carlo Trombetti, Cristina |
| author_facet | Celentano, Antonio Nitsch, Carlo Trombetti, Cristina |
| contents | In this paper, we establish a comparison principle in terms of Lorentz norms and point-wise inequalities between a positive solution $u$ to the Poisson equation with non-homogeneous Neumann boundary conditions and a specific positive solution $v$ to the Schwartz symmetrized problem, which is related to $u$ through an additional boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Talenti comparison result for a class of Neumann boundary value problems Celentano, Antonio Nitsch, Carlo Trombetti, Cristina Analysis of PDEs 35B09, 35B51, 35D30, 35J05 In this paper, we establish a comparison principle in terms of Lorentz norms and point-wise inequalities between a positive solution $u$ to the Poisson equation with non-homogeneous Neumann boundary conditions and a specific positive solution $v$ to the Schwartz symmetrized problem, which is related to $u$ through an additional boundary condition. |
| title | A Talenti comparison result for a class of Neumann boundary value problems |
| topic | Analysis of PDEs 35B09, 35B51, 35D30, 35J05 |
| url | https://arxiv.org/abs/2405.05392 |