Further Time Regularity for Non-Local, Fully Non-Linear Parabolic Equations

TL;DR

This paper develops new regularity estimates for solutions to non-local, fully non-linear parabolic equations, extending classical results to rough kernels and broad boundary conditions.

Contribution

It introduces H"older estimates for the time derivative and extends Evans-Krylov estimates to a wider class of non-local parabolic equations with rough kernels.

Findings

Established H"older continuity for time derivatives of solutions.

Extended Evans-Krylov estimates to non-local, rough kernel cases.

Provided regularity results under mild boundary data assumptions.

Abstract

We establish H\"older estimates for the time derivative of solutions of non-local parabolic equations under mild assumptions for the boundary data. As a consequence we are able to extend the Evans-Krylov estimate for rough kernels to parabolic equations.