Regularity results for nonlocal equations by approximation

TL;DR

This paper establishes a nonlocal version of classical regularity estimates and applies them to extend regularity results for fully nonlinear integro-differential equations with variable coefficients.

Contribution

It introduces a nonlocal Cordes-Niremberg estimate and extends regularity results to variable coefficient cases and other perturbed settings.

Findings

Proves a nonlocal Cordes-Niremberg estimate.

Extends regularity results to variable coefficient equations.

Applicable to perturbed translation-invariant equations.

Abstract

In this paper we prove a nonlocal version of the Cordes-Niremberg estimates. We use it to extend our previous regularity results for fully nonlinear integro-differential equations to the variable coefficient case and several other settings where the equation can be thought of as a perturbation of the translation invariant case.