Openness of shape optimizers in higher-order and non-scalar problems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908561508925440 |
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| author | Frank, Rupert L. |
| author_facet | Frank, Rupert L. |
| contents | We consider the first eigenvalues of the polyharmonic, Lamé and Stokes operators with Dirichlet boundary conditions on sets of given finite measure. It is shown that a quasi-open set for which this eigenvalue is minimal is open. This removes dimensional restrictions in earlier works. We use Campanato theory, which works well in the present higher order or non-scalar setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Openness of shape optimizers in higher-order and non-scalar problems Frank, Rupert L. Analysis of PDEs Spectral Theory We consider the first eigenvalues of the polyharmonic, Lamé and Stokes operators with Dirichlet boundary conditions on sets of given finite measure. It is shown that a quasi-open set for which this eigenvalue is minimal is open. This removes dimensional restrictions in earlier works. We use Campanato theory, which works well in the present higher order or non-scalar setting. |
| title | Openness of shape optimizers in higher-order and non-scalar problems |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2509.22487 |