Small perturbation solutions for nonlocal elliptic equations

We present a small perturbation result for nonlocal elliptic equations, which says that for a class of nonlocal operators, the solutions are in $C^{σ+α}$ for any $α\in (0,1)$ 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.

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