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

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 derive quantitatively the Harnack inequalities for kinetic integro-differential equations.
This implies Hölder continuity. Our method is based on trajectories and exploits a term …

We deal with a wide class of kinetic equations, $$\big [\partial_t+ v\cdot\nabla_x\big]
f=\mathcal {L} _v f. $$ Above, the diffusion term $\mathcal {L} _v $ is an integro-differential …

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 study local boundedness and Hölder continuity of a parabolic equation involving the
fractional p-Laplacian of order s, with 0< s< 1, 2≤ p<∞, with a general right-hand side. We …

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 …