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 …

We consider minimizers of where F is a function strictly increasing in each parameter, and is
the kth Dirichlet eigenvalue of Ω. Our main result is that the reduced boundary of the …

In this paper we study the free boundary regularity for almost-minimizers of the functional J
(u)=∫ Ω|∇ u (x)| 2+ q+ 2 (x) χ {u> 0}(x)+ q− 2 (x) χ {u< 0}(x) dx where q±∈ L∞(Ω). Almost …

In this paper we prove the rectifiability of and measure bounds on the singular set of the free-
boundary for minimizers of a functional first considered by Alt–Caffarelli [J. Reine Angew …

The objective of this paper is two-fold. First, we establish new sharp quantitative estimates
for Faber-Krahn inequalities on simply connected space forms. We prove that the gap …

We consider minimizers of where F is a function nondecreasing in each parameter, and λk
(Ω) is the kth Dirichlet eigenvalue of ω. This includes, in particular, functions F that depend …

Regularity of the free boundary for the vectorial Bernoulli problem Page 1 ANALYSIS & PDE
msp Volume 13 No. 3 2020 DARIO MAZZOLENI, SUSANNA TERRACINI AND BOZHIDAR …

Using a direct approach, we prove a two‐dimensional epiperimetric inequality for the one‐
phase problem in the scalar and vectorial cases and for the double‐phase problem. From …

This paper is dedicated to the study of shape optimization problems for the first eigenvalue
of the elliptic operator with drift L=-Δ+ V (x) ⋅ ∇ L=-Δ+ V (x)·∇ with Dirichlet boundary …

We study the existence and structure of branch points in two-phase free boundary problems.
More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type …