This paper is concerned with the structure of Gromov-Hausdorff limit spaces
(M^n_i,g_i,p_i)d_GH⟶(X^n,d,p) of Riemannian manifolds satisfying a uniform lower Ricci …

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-
phase free boundary problem. The problem of classifying stable (or minimal) homogeneous …

We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli
problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a …

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 study viscosity solutions to the classical one-phase problem and its thin counterpart. In
low dimensions, we show that when the free boundary is the graph of a continuous function …

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 …

Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric
measure theory. The last four decades have seen the emergence of a wealth of connections …

Free boundaries occur in a lot of physical phenomena and are of major interest both
mathematically and physically. The aim of this contribution is to describe new ideas and …

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 …

Let u be a harmonic function in a C 1-Dini domain D⊂ R d such that u vanishes on a
boundary surface ball∂ D∩ B 5 R (0). We consider an effective version of its singular set …