Abstract

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 C1C^1 boundary.

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Keywords

  • Robin Laplacian
  • eigenvalues
  • shape optimization
  • convex domains

Mathematics Subject Classification

49Q10, 49R05

References

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Suggested citation

S. Cito. “Existence and Regularity of Optimal Convex Shapes for Functionals Involving the Robin Eigenvalues.” Journal of Convex Analysis 26 (2019), No. 3, 925–943. https://doi.org/10.68381/jca26050

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Published by Heldermann Verlag, 2019. Rights now held by Banach Press LLC.