A nonlocal anisotropic eigenvalue problem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866929529570721792 |
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| author | Piscitelli, Gianpaolo |
| author_facet | Piscitelli, Gianpaolo |
| contents | We determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using also some properties related to the associated \lq\lq twisted\rq\rq problem, we show that, this problem displays a \emph{saturation} phenomenon: the first eigenvalue increases with the weight up to a critical value and then remains constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_03768 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A nonlocal anisotropic eigenvalue problem Piscitelli, Gianpaolo Analysis of PDEs 35P15, 49R50 We determine the shape which minimizes, among domains with given measure, the first eigenvalue of the anisotropic laplacian perturbed by an integral of the unknown function. Using also some properties related to the associated \lq\lq twisted\rq\rq problem, we show that, this problem displays a \emph{saturation} phenomenon: the first eigenvalue increases with the weight up to a critical value and then remains constant. |
| title | A nonlocal anisotropic eigenvalue problem |
| topic | Analysis of PDEs 35P15, 49R50 |
| url | https://arxiv.org/abs/2008.03768 |