Dini estimates for nonlocal fully nonlinear elliptic equations

TL;DR

This paper establishes Dini continuity estimates for a class of nonlocal fully nonlinear elliptic equations with rough kernels, advancing the understanding of their regularity properties.

Contribution

It introduces a new approach using Campanato's method and refines existing $C^{\sigma+\alpha}$ estimates for nonlocal equations with non-symmetric kernels.

Findings

Dini estimates for nonlocal elliptic equations are achieved.

The method applies to equations with rough, non-symmetric kernels.

Refined regularity estimates improve understanding of solution smoothness.

Abstract

We obtain Dini type estimates for a class of concave fully nonlinear nonlocal elliptic equations of order $\sigma\in (0,2)$ with rough and non-symmetric kernels. The proof is based on a novel application of Campanato's approach and a refined $C^{\sigma+\alpha}$ estimate in [8].