Openness of shape optimizers in higher-order and non-scalar problems
Analysis of PDEs
2025-09-29 v1 Spectral Theory
Abstract
We consider the first eigenvalues of the polyharmonic, Lam\'e 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.
Keywords
Cite
@article{arxiv.2509.22487,
title = {Openness of shape optimizers in higher-order and non-scalar problems},
author = {Rupert L. Frank},
journal= {arXiv preprint arXiv:2509.22487},
year = {2025}
}
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12 pages