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Existence and Regularity Results for...
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Velichkov, Bozhidar.
Existence and Regularity Results for Some Shape Optimization Problems
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Existence and Regularity Results for Some Shape Optimization Problems/ by Bozhidar Velichkov.
Author:
Velichkov, Bozhidar.
Description:
XVI, 349 p.online resource. :
Contained By:
Springer Nature eBook
Subject:
Calculus of variations. -
Online resource:
https://doi.org/10.1007/978-88-7642-527-1
ISBN:
9788876425271
Existence and Regularity Results for Some Shape Optimization Problems
Velichkov, Bozhidar.
Existence and Regularity Results for Some Shape Optimization Problems
[electronic resource] /by Bozhidar Velichkov. - 1st ed. 2015. - XVI, 349 p.online resource. - Theses (Scuola Normale Superiore),192239-1460 ;. - Theses (Scuola Normale Superiore),19.
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. .
ISBN: 9788876425271
Standard No.: 10.1007/978-88-7642-527-1doiSubjects--Topical Terms:
527927
Calculus of variations.
LC Class. No.: QA315-316
Dewey Class. No.: 515.64
Existence and Regularity Results for Some Shape Optimization Problems
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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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