Existence and regularity results for solutions of spectral problems
Dario Mazzoleni · 2014
This Thesis is devoted to the study of some shape optimization problems for eigenvalues of the Dirichlet Laplacian. In particular we prove that there exists an optimal set for the kth eigenvalue of the Dirichlet Laplacian among quasi open sets of R^N and that this set admits an eigenfunction, corresponding to lambda_k, which is Lipschitz continuous in R^N.