Symmetrization results for general nonlocal linear ellipitic and parabolic problems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909337791758336 |
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| author | Ferone, Vincenzo Piscitelli, Gianpaolo Volzone, Bruno |
| author_facet | Ferone, Vincenzo Piscitelli, Gianpaolo Volzone, Bruno |
| contents | We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions. In this framework, the relevant concentration comparison for the classical fractional Laplacian can be reviewed as a special case of our main result, thus generalizing the previous results in [21]. Finally, using an implicit time discretization techniques, similar results are obtained for the solutions of Cauchy-Dirichlet nonlocal linear parabolic problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00632 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetrization results for general nonlocal linear ellipitic and parabolic problems Ferone, Vincenzo Piscitelli, Gianpaolo Volzone, Bruno Analysis of PDEs We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions. In this framework, the relevant concentration comparison for the classical fractional Laplacian can be reviewed as a special case of our main result, thus generalizing the previous results in [21]. Finally, using an implicit time discretization techniques, similar results are obtained for the solutions of Cauchy-Dirichlet nonlocal linear parabolic problems. |
| title | Symmetrization results for general nonlocal linear ellipitic and parabolic problems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2311.00632 |