Existence of an optimal shape for the first eigenvalue of polyharmonic operators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915102522867712 |
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| author | Leylekian, Roméo |
| author_facet | Leylekian, Roméo |
| contents | We prove the existence of an open set minimizing the first eigenvalue of the Dirichlet polylaplacian of order $m\geq1$ under volume constraint. Moreover, the corresponding eigenfunction is shown to enjoy $C^{m-1,α}$ Hölder regularity. This is performed for dimension $2\leq d\leq 4m$. In particular, our analysis answers the question of the existence of an optimal shape for the clamped plate up to dimension $8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11713 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of an optimal shape for the first eigenvalue of polyharmonic operators Leylekian, Roméo Analysis of PDEs Optimization and Control 35P05, 35G15, 49R05, 49J30 We prove the existence of an open set minimizing the first eigenvalue of the Dirichlet polylaplacian of order $m\geq1$ under volume constraint. Moreover, the corresponding eigenfunction is shown to enjoy $C^{m-1,α}$ Hölder regularity. This is performed for dimension $2\leq d\leq 4m$. In particular, our analysis answers the question of the existence of an optimal shape for the clamped plate up to dimension $8$. |
| title | Existence of an optimal shape for the first eigenvalue of polyharmonic operators |
| topic | Analysis of PDEs Optimization and Control 35P05, 35G15, 49R05, 49J30 |
| url | https://arxiv.org/abs/2402.11713 |