Interior regularity for nonlocal fully nonlinear equations with Dini continuous terms

TL;DR

This paper establishes interior regularity results for viscosity solutions of nonlocal fully nonlinear equations with Dini continuous terms, using perturbative methods and a recursive Evans-Krylov theorem.

Contribution

It introduces new regularity estimates for nonlocal equations with Dini continuous terms, extending previous results to non-translation invariant cases.

Findings

Achieved $C^{\sigma}$ regularity estimates for solutions.

Developed a perturbative approach for nonlocal equations.

Extended Evans-Krylov theorem to non-translation invariant settings.

Abstract

This paper is concerned with interior regularity of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations with Dini continuous terms. We obtain $C^{\sigma}$ regularity estimates for the nonlocal equations by perturbative methods and a version of a recursive Evans-Krylov theorem.