Schauder estimates for nonlocal fully nonlinear equations

TL;DR

This paper develops Schauder estimates for solutions to nonlocal fully nonlinear elliptic equations, using perturbative methods and a recursive Evans-Krylov theorem to handle translation invariant cases.

Contribution

It introduces a novel recursive Evans-Krylov theorem and applies perturbative techniques to establish Schauder estimates for nonlocal fully nonlinear equations.

Findings

Established pointwise Schauder estimates for nonlocal equations

Developed a recursive Evans-Krylov theorem for translation invariant cases

Provided a new approach for regularity in nonlocal nonlinear PDEs

Abstract

In this paper, we establish pointwise Schauder estimates for solutions of nonlocal fully nonlinear elliptic equations by perturbative arguments. A key ingredient is a recursive Evans-Krylov theorem for nonlocal fully nonlinear translation invariant equations.