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

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