| Existence and Regularity Results for Some Shape Optimization Problems Contributor(s): Velichkov, Bozhidar (Author) |
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ISBN: 8876425268 ISBN-13: 9788876425264 Publisher: Edizioni Della Normale OUR PRICE: $23.74 Product Type: Paperback Published: April 2015 |
| Additional Information |
| BISAC Categories: - Mathematics | Optimization - Mathematics | Calculus |
| Dewey: 515.64 |
| Physical Information: 1.1" H x 6" W x 9.4" (1.40 lbs) 349 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schr dinger 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. |