Existence and Regularity Results for Some Shape Optimization Problems
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...
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| Ngôn ngữ: | English |
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2015
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58190 |
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oai:scholar.dlu.edu.vn:DLU123456789-581902023-11-11T06:03:43Z Existence and Regularity Results for Some Shape Optimization Problems Velichkov, Bozhidar Applied Mathematics Function spaces Mathematical optimization 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. 2015-09-10T09:53:44Z 2015-09-10T09:53:44Z 2015 Book 978-88-7642-527-1 978-88-7642-526-4 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58190 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Applied Mathematics Function spaces Mathematical optimization |
| spellingShingle |
Applied Mathematics Function spaces Mathematical optimization Velichkov, Bozhidar Existence and Regularity Results for Some Shape Optimization Problems |
| description |
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. |
| format |
Book |
| author |
Velichkov, Bozhidar |
| author_facet |
Velichkov, Bozhidar |
| author_sort |
Velichkov, Bozhidar |
| title |
Existence and Regularity Results for Some Shape Optimization Problems |
| title_short |
Existence and Regularity Results for Some Shape Optimization Problems |
| title_full |
Existence and Regularity Results for Some Shape Optimization Problems |
| title_fullStr |
Existence and Regularity Results for Some Shape Optimization Problems |
| title_full_unstemmed |
Existence and Regularity Results for Some Shape Optimization Problems |
| title_sort |
existence and regularity results for some shape optimization problems |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58190 |
| _version_ |
1782535924260798464 |