| 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 |  |
| 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 |
| doi | https://doi.org/10.1007/978-88-7642-527-1 |
| isbn_softcover | 978-88-7642-526-4 |
| isbn_ebook | 978-88-7642-527-1Series ISSN 2239-1460 Series E-ISSN 2532-1668 |
| issn_series | 2239-1460 |
| copyright | Scuola Normale Superiore Pisa 2015 |
发表于 2025-3-21 17:02:48
