We complete the local regularity program for weak solutions to linear parabolic nonlocal
equations with bounded measurable coefficients. Within the variational framework we prove …

Local boundedness and Harnack inequalities are studied for solutions to parabolic and
elliptic integrodifferential equations whose governing nonlocal operators are associated with …

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 …

We study integro‐differential elliptic equations (of order 2 s 2s) with variable coefficients, and
prove the natural and most general Schauder‐type estimates that can hold in this setting …

We prove trace and extension results for fractional Sobolev spaces of order s∈(0, 1). These
spaces are used in the study of nonlocal Dirichlet and Neumann problems on bounded …

The purpose of this paper is to prove new fine regularity results for nonlocal drift-diffusion
equations via pointwise potential estimates. Our analysis requires only minimal assumptions …

We derive the Strong Harnack inequality for a class of hypoelliptic integro-differential
equations in divergence form. The proof is based on a priori estimates, and as such extends …

We study continuous time random walks on $\mathbb {Z}^ d $(with $ d\geq 2$) among
random conductances $\{\omega (\{x, y\}): x, y\in\mathbb {Z}^ d\} $ that permit jumps of …

In this paper we study interior potential-theoretic properties of purely discontinuous Markov
processes in proper open subsets D⊂ R d. The jump kernels of the processes may be …

We prove well-posedness, Harnack inequality and sharp regularity of solutions to a
fractional $ p $-Laplace non-homogeneous equation $(-\Delta_p)^ su= f $, with $0< s< 1 …