Seminario di analisi matematica
ore
15:00
presso Seminario II
In this talk we study 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 Schr\"odinger
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.