In this article we consider a class of non-degenerate elliptic operators obtained by
superpositioning the Laplacian and a general nonlocal operator. We study the existence …

We consider Dirichlet exterior value problems related to a class of nonlocal Schrödinger
operators, whose kinetic terms are given in terms of Bernstein functions of the Laplacian. We …

We consider a class of diffusions controlled through the drift and jump size, and driven by a
jump Lévy process and a nondegenerate Wiener process, and we study infinite horizon …

This paper is concerned with existence of a C^ α C α viscosity solution of a second order
non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such …

Abstract Aleksandrov–Bakelman–Pucci maximum principles are studied for a class of fully
nonlinear integro-differential equations of order σ ∈ 2-ε _0, 2) σ∈ 2-ε 0, 2), where ε _0 ε 0 is …

Integro-differential operators arise naturally in biological modeling and mathematical
finance. We aim to conduct an in-depth study of integro-differential operators and their …

We consider Dirichlet exterior value problems related to a class of non-local Schr odinger
operators, whose kinetic terms are given in terms of Bernstein functions of the Laplacian. We …