SEMINARIO DI ANALISI MATEMATICA
https://sites.google.com/view/seminarioanalisiunimi/

 

Nell’ambito del seminario di Analisi Matematica del Dipartimento di Matematica “Federigo Enriques"

 

Mercoledì 11 Dicembre alle 14:30

presso l'Aula C del Dipartimento di Matematica dell'Università  di Milano
si terrà il seguente seminario:

Dario Mazzoleni
(Università Cattolica del Sacro Cuore)

 

Optimization results for the higher eigenvalues of the $p$-Laplacian

 

Abstract: 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. This is a joint work with Marco Degiovanni.