Regularity of the One-phase Free Boundaries

This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the on…

Regularity of the One-phase Free Boundaries

Edition

-

ISBN/ISSN

978-3-031-13237-7

Collation

-

Series Title

-

Call Number

-

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. We investigate the properties of the optimal sets and of the optimal state functions. In par…