Publications of the Scuola Normale Superiore

Velichkov, Bozhidar

​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 optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems.

Details

Published by: Edizioni della Normale

Publication Date: 2015-04-15

Format: Paperback

ISBN-13: 9788876425264

DOI: 10.1007/978-88-7642-527-1

Dimensions: 240cm x150cm

Pages: 349