Regularity results for fully nonlinear parabolic integro-differential operators

TL;DR

This paper develops regularity theory for fully nonlinear parabolic integro-differential equations with symmetric kernels, establishing key estimates and regularity results including Harnack inequality and Hölder continuity.

Contribution

It introduces parabolic versions of classical estimates and regularity results for a broad class of nonlinear integro-differential equations with symmetric kernels.

Findings

Established parabolic Alexandrov-Bakelman-Pucci estimate for 0<σ<2

Proved Harnack inequality for solutions

Demonstrated Hölder and C^{1,α} regularity of solutions

Abstract

In this paper, we consider the regularity theory for fully nonlinear parabolic integro-differential equations with symmetric kernels. We are able to find parabolic versions of Alexandrov-Backelman-Pucci estimate with 0<\sigma<2. And we show a Harnack inequality, H\"older regularity, and C^{1,\alpha}-regularity of the solutions by obtaining decay estimates of their level sets.