Journal of the London Mathematical Society ( IF 1.121 ) Pub Date : 2021-01-12 , DOI: 10.1112/jlms.12425
Marco Degiovanni; Dario Mazzoleni

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 $γ$‐convergence.

p-Laplacian较高特征值与符号更改容量度量相关的优化结果

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