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Existence and regularity results for...

Velichkov, Bozhidar.

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Existence and regularity results for some shape optimization problems

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Existence and regularity results for some shape optimization problems/ by Bozhidar Velichkov.
作者:	Velichkov, Bozhidar.
出版者:	Pisa :Scuola Normale Superiore : : 2015.,
面頁冊數:	xvi, 349 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Mathematical optimization. -
電子資源:	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:

517763
Mathematical optimization.

LC Class. No.: QA402.5

Dewey Class. No.: 519.6

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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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