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Titlebook: Existence and Regularity Results for Some Shape Optimization Problems; Bozhidar Velichkov Book 2015 Scuola Normale Superiore Pisa 2015 Sch

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发表于 2025-3-21 17:02:48 | 显示全部楼层 |阅读模式
书目名称Existence and Regularity Results for Some Shape Optimization Problems
编辑Bozhidar Velichkov
视频video
概述Provides a detailed and self-contained introduction to the recent results and techniques in shape optimization.Presents new techniques concerning the regularity of the optimal sets.Self-contained expo
丛书名称Publications of the Scuola Normale Superiore
图书封面Titlebook: Existence and Regularity Results for Some Shape Optimization Problems;  Bozhidar Velichkov Book 2015 Scuola Normale Superiore Pisa 2015 Sch
描述​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. 
出版日期Book 2015
关键词Schrödinger operators; eigenfunctions; optimal sets; optimal state functions; spectral optimization prob
版次1
doihttps://doi.org/10.1007/978-88-7642-527-1
isbn_softcover978-88-7642-526-4
isbn_ebook978-88-7642-527-1Series ISSN 2239-1460 Series E-ISSN 2532-1668
issn_series 2239-1460
copyrightScuola Normale Superiore Pisa 2015
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发表于 2025-3-21 23:17:20 | 显示全部楼层
2239-1460 t 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. 978-88-7642-526-4978-88-7642-527-1Series ISSN 2239-1460 Series E-ISSN 2532-1668
发表于 2025-3-22 00:33:29 | 显示全部楼层
https://doi.org/10.1007/978-88-7642-527-1Schrödinger operators; eigenfunctions; optimal sets; optimal state functions; spectral optimization prob
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https://doi.org/10.1007/978-3-8349-6180-8 model problem.where . > 0 is a given constant. The existence of an optimal set for the problem (6.1) was proved recently by Bucur (see [20]) and by Mazzoleni and Pratelli (see [81])two completely different techniques.
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https://doi.org/10.1007/978-3-476-99593-3s in the Euclidean space ℝ., allowing us to threat at once problems concerning elliptic problems on domains, Schrödinger operators and operators involving traces of Sobolev functions on (. − 1)-dimensional sets.
发表于 2025-3-23 08:11:16 | 显示全部楼层
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