Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts

TL;DR

This paper establishes Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with rough kernels and drifts, extending previous work to include equations with measurable coefficients and non-symmetric kernels.

Contribution

It introduces new Dini and Schauder estimates for a broader class of nonlocal parabolic equations, including those with rough, non-symmetric kernels and measurable coefficients.

Findings

Derived Dini and Schauder estimates for nonlocal equations with rough kernels

Extended estimates to equations with measurable coefficients in time

Analyzed equations with non-symmetric kernels

Abstract

We obtain Dini and Schauder type estimates for concave fully nonlinear nonlocal parabolic equations of order $\sigma\in (0,2)$ with rough and non-symmetric kernels, and drift terms. We also study such linear equations with only measurable coefficients in the time variable, and obtain Dini type estimates in the spacial variable. This is a continuation of the work [10, 11] by the first and last authors.