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Book synopsis

żWe 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. 

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Existence and Regularity Results for Some Shape Optimization Problems
• Author: Bozhidar Velichkov
• Language: English
• Binding: Paperback
• Number of pages: 349
• EAN: 9788876425264
• ISBN: 9788876425264
• ID: 03606893
• Publisher: Birkhauser Verlag AG
• Weight: 635 g
• Dimensions: 240 × 150 × 28 mm
• Date of publishing: 09. April 2015

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