Regularity results for nonlocal parabolic equations

TL;DR

This paper surveys recent advances in the regularity theory of nonlocal parabolic equations, extending previous results to more general kernels and providing new estimates for solutions.

Contribution

It extends existing regularity results to nonlocal operators with non-absolutely continuous kernels, broadening the scope of known estimates.

Findings

Extended regularity estimates to nonlocal operators with singular kernels

Built upon Felsinger-Kassmann (2013) results

Provided new bounds for solutions of nonlocal parabolic equations

Abstract

We survey recent regularity results for parabolic equations involving nonlocal operators like the fractional Laplacian. We extend the results of Felsinger-Kassmann (2013) and obtain regularity estimates for nonlocal operators with kernels not being absolutely continuous with respect to the Lebesgue measure.