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

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 …

We prove precise rates of convergence for monotone approximation schemes of fractional
and nonlocal Hamilton–Jacobi–Bellman equations. We consider diffusion-corrected …

We study discretizations of fractional fully nonlinear equations by powers of discrete
Laplacians. Our problems are parabolic and of order σ∈(0, 2) since they involve fractional …

In this article we study for the first time the regularity of the free boundary in the one-phase
free boundary problem driven by a general nonlocal operator. Our main results establish …

We establish a Talenti-type symmetrization result in the form of mass concentration (ie
integral comparison) for very general linear nonlocal elliptic problems, equipped with …

In this chapter, we study obstacle problems for nonlocal elliptic operators. In order to do so,
we first prove the boundary Harnack inequality for such operators in Lipschitz domains, a …