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arXiv · 1609.01375

Small perturbation solutions for nonlocal elliptic equations

Hui Yu
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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.

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Hui Yu. 2016-09-06. Small perturbation solutions for nonlocal elliptic equations. https://arxiv.org/abs/1609.01375

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