Existence And Regularity Results For Some Shape Optimization Problems
Download and Read Existence And Regularity Results For Some Shape Optimization Problems full books in PDF, ePUB, and Kindle. Read online free Existence And Regularity Results For Some Shape Optimization Problems ebook anywhere anytime directly on your device. We cannot guarantee that every ebooks is available!
Existence and Regularity Results for Some Shape Optimization Problems
Author | : Bozhidar Velichkov |
Publisher | : Springer |
Total Pages | : 362 |
Release | : 2015-03-21 |
Genre | : Mathematics |
ISBN | : 8876425276 |
Download Existence and Regularity Results for Some Shape Optimization Problems Book in PDF, Epub and Kindle
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.