Progress in Mathematics is a series of books intended for professional mathematicians and
scientists, encompassing all areas of pure mathematics. This distinguished series, which …

We study solutions to L u= f in Ω⊂ R n, being L the generator of any, possibly non-
symmetric, stable Lévy process. On the one hand, we study the regularity of solutions to L u …

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 Besov regularity estimates for the solution of the Dirichlet problem involving the
integral fractional Laplacian of order s in bounded Lipschitz domains Ω:‖ u‖ B˙ 2,∞ s+ r …

In this article a nonlocal analogue of an inverse problem in diffuse optical tomography is
considered. We show that whenever one has given two pairs of diffusion and absorption …

Despite significant recent advances in the regularity theory for obstacle problems with
integro-differential operators, some fundamental questions remained open. On the one …

In this paper we establish for the first time local semiconvexity estimates for fully nonlinear
equations and for obstacle problems driven by integro-differential operators with general …

In this paper we establish optimal regularity estimates and smoothness of free boundaries
for nonlocal obstacle problems governed by a very general class of integro-differential …

In this article we establish for the first time the $ C^ s $ boundary regularity of solutions to
nonlocal elliptic equations with kernels $ K (y)\asymp| y|^{-n-2s} $. This was known to hold …

In this article we prove for the first time the $ C^ s $ boundary regularity for solutions to
nonlocal elliptic equations with H\" older continuous coefficients in divergence form in …