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Existence and regularity results for some shape optimization problems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Existence and regularity results for some shape optimization problemsby Bozhidar Velichkov.
Author:	Velichkov, Bozhidar.
Published:	Pisa :Scuola Normale Superiore :2015.
Description:	xvi, 349 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Mathematical optimization.
Online resource:	http://dx.doi.org/10.1007/978-88-7642-527-1
ISBN:	9788876425271 (electronic bk.)

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. - Pisa :Scuola Normale Superiore :2015. - xvi, 349 p. :ill., digital ;24 cm. - Publications of the scuola normale superiore ;19. - Publications of the scuola normale superiore ;5..

We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrodinger 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 (electronic bk.)

Standard No.: 10.1007/978-88-7642-527-1doiSubjects--Topical Terms:

183292
Mathematical optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

Existence and regularity results for some shape optimization problems
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520 $a We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrodinger 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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