In this paper we prove the existence of an optimal set for the minimization of the k th variational eigenvalue of the p-Laplacian among p-quasi open sets of fixed measure included in a box of finite measure. An analogous existence result is obtained for eigenvalues of the p-Laplacian associated with Schrödinger potentials. In order to deal with these nonlinear shape optimization problems, we develop a general approach which allows to treat the continuous dependence of the eigenvalues of the p-Laplacian associated with sign-changing capacitary measures under gamma -convergence.

Optimization results for the higher eigenvalues of the p-Laplacian associated with sign-changing capacitary measures

Mazzoleni D.
2021

Abstract

In this paper we prove the existence of an optimal set for the minimization of the k th variational eigenvalue of the p-Laplacian among p-quasi open sets of fixed measure included in a box of finite measure. An analogous existence result is obtained for eigenvalues of the p-Laplacian associated with Schrödinger potentials. In order to deal with these nonlinear shape optimization problems, we develop a general approach which allows to treat the continuous dependence of the eigenvalues of the p-Laplacian associated with sign-changing capacitary measures under gamma -convergence.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/1440635
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