TY  - GEN
TY  - GEN
T1  - Existence and Regularity Results for Some Shape Optimization Problems
T2  - Theses (Scuola Normale Superiore),
A1  - Velichkov, Bozhidar.
LA  - English
PP  - Pisa
PB  - Scuola Normale Superiore : Imprint: Edizioni della Normale
YR  - 2015
ED  - 1st ed. 2015.
UL  - http://discoverylib.upm.edu.my/discovery/Record/978-88-7642-527-1
AB  - 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. .
OP  - 349
CN  - QA315-316
SN  - 9788876425271
KW  - Calculus of variations.
KW  - Calculus of Variations and Optimal Control; Optimization.
ER  -