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Article Dans Une Revue Communications in Analysis and Geometry Année : 2019

Regularity result for a shape optimization problem under perimeter constraint

Résumé

We study the problem of optimizing the eigenvalues of the Dirichlet Laplace operator under perimeter constraint. We prove that optimal sets are analytic outside a closed singular set of dimension at most d−8 by writing a general optimality condition in the case the optimal eigenvalue is multiple. As a consequence we find that the optimal k-th eigenvalue is strictly smaller than the optimal (k + 1)-th eigenvalue. We also provide an elliptic regularity result for sets with positive and bounded weak curvature.
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Dates et versions

hal-03181142 , version 1 (25-03-2021)

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Beniamin Bogosel. Regularity result for a shape optimization problem under perimeter constraint. Communications in Analysis and Geometry, 2019, 27 (7), pp.1523-1547. ⟨10.4310/CAG.2019.v27.n7.a3⟩. ⟨hal-03181142⟩
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