Existence and Regularity Results fo - E-book

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Existence And Regularity Results For Some Shape Optimization Problems - ENG

Bozhidar Velichkov

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Sinopsis

ISBN:	9788876425271
Formato:	Page Fidelity
Idioma:	Inglés
Editorial:	Springer Nature
Tema:	Matemáticas
Subtema:	Optimización
Año de publicación:	2015-03-21

â€‹We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or ofÂ more general SchrÃ¶dinger 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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