$L^p$-solvability of nonlocal parabolic equations with spatial dependent and non-smooth kernelsXiche

TL;DR

This paper establishes the optimal $L^p$-solvability for nonlocal parabolic equations with spatially dependent, non-smooth kernels, advancing the understanding of such equations in mathematical analysis.

Contribution

It proves the optimal $L^p$-solvability for a class of nonlocal parabolic equations with complex kernels, which was previously unresolved.

Findings

Proved optimal $L^p$-solvability for nonlocal parabolic equations

Extended solvability results to equations with non-smooth, spatially dependent kernels

Provided new analytical techniques for nonlocal PDEs

Abstract

In this paper we prove the optimal $L^p$-solvability of nonlocal parabolic equation with spatial dependent and non-smooth kernels.