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 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 …

We prove an optimal extension and trace theorem for Sobolev spaces of nonlocal operators.
The extension is given by a suitable Poisson integral and solves the corresponding nonlocal …

Barriers, exit time and survival probability for unimodal Lévy processes | Probability Theory
and Related Fields Skip to main content SpringerLink Log in Menu Find a journal Publish with …

We consider a large class of symmetric pure jump Markov processes dominated by isotropic
unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided …

In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the
potential kernel and the Green function for a ball for general isotropic unimodal Lévy …

We study the asymptotic formulas and estimates for the transition densities of isotropic
unimodal convolution semigroups of probability measures on under the assumption that its …

We study the overdetermined problem for a large family of non-local operators given by
generators of subordinate Brownian motions. In particular, this family includes the fractional …

We derive a lower bound on the location of global extrema of eigenfunctions for a large
class of non-local Schrödinger operators in convex domains under Dirichlet exterior …

We consider a large family of integro-differential equations and establish a non-local
counterpart of Hopf's lemma, directly expressed in terms of the symbol of the operator. As …