ENGLISH

Existence and Regularity Results for Some Shape Optimization Problems

By Bozhidar Velichkov (auth.)

Book information

Publisher
Edizioni della Normale
Year
2015
ISBN
978-88-7642-526-4, 978-88-7642-527-1
DOI
10.1007/978-88-7642-527-1
Language
english
Format
PDF
Filesize
2 MB (2422956 bytes)
Series
Publications of the Scuola Normale Superiore 19
Edition
1
Pages
349\362
Time added
2015-04-23 16:00:00
Calculus of Variations and Optimal Control; Optimi

Description

​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.

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