Small perturbation solutions for nonlocal elliptic equations

Abstract

We present a small perturbation result for nonlocal elliptic equations, which says that for a class of nonlocal operators, the solutions are in $C^{\sigma +\alpha }$ for any $\alpha \in (0,1)$ as long as the solutions are small. This is a nonlocal generalization of a celebrated result of Savin in the case of second order equations.

15 pages. Submitted