Existence and Regularity Results for Some Shape Optimization Problems - Bozhidar Velichkov Kartoniert (TB)

We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optim ization problems in non-Euclidean settings and optimization problems for potentials and measures as well as multiphase and optimal partition problems.