Calder\'on-Zygmund theory of nonlocal parabolic equations with discontinuous coefficients

TL;DR

This paper establishes Calderón-Zygmund estimates for weak solutions to nonlocal parabolic equations with discontinuous coefficients, showing increased fractional differentiability despite minimal regularity assumptions.

Contribution

It introduces Calderón-Zygmund estimates for nonlocal parabolic equations with minimal regularity on coefficients, revealing enhanced fractional differentiability of solutions.

Findings

Calderón-Zygmund estimates are proved for nonlocal parabolic equations.

Solutions exhibit increased fractional differentiability despite discontinuous coefficients.

The results apply to equations with fractional Laplacian type data and non-divergence data.

Abstract

We prove Calder\'on-Zygmund type estimates of weak solutions to non-homogeneous nonlocal parabolic equations under a minimal regularity requirement on kernel coefficients. In particular, the right-hand side is presented by a sum of fractional Laplacian type data and a non-divergence type data. Interestingly, even though the kernel coefficients are discontinuous, we obtain a significant increment of fractional differentiability for the solutions, which is not observed in the corresponding local parabolic equations.