Journal of Convex Analysis 26 (2019), No. 3, 925--943
Copyright Heldermann Verlag 2019
Existence and Regularity of Optimal Convex Shapes for Functionals Involving the Robin Eigenvalues
Dip. di Matematica e Fisica, UniversitÓ del Salento, 73100 Lecce, Italia
We study the existence and the regularity of optimal convex domains for a large class of shape optimization problems involving functions of the eigenvalues of the Robin-Laplacian on convex sets. We will prove that convex solutions exist and that, under some additional hypotheses on the functional, these optimal sets have C1 boundary.
Keywords: Robin Laplacian, eigenvalues, shape optimization, convex domains.
MSC: 49Q10, 49R05.
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