Higher H\"older regularity for nonlocal parabolic equations with irregular kernels

TL;DR

This paper proves higher H"older regularity for solutions to nonlocal parabolic equations with irregular kernels, under certain integrability conditions and minimal kernel regularity assumptions.

Contribution

It introduces new regularity results for nonlocal parabolic equations with irregular kernels, relaxing previous kernel regularity requirements.

Findings

Higher H"older regularity established for solutions

Regularity results hold under weaker kernel assumptions

Requires higher integrability of nonhomogeneous terms

Abstract

We study a nonlocal parabolic equation with an irregular kernel coefficient to establish higher H\"older regularity under an appropriate higher integrablilty on the nonhomogeneous terms and a minimal regularity assumption on the kernel coefficient.