Non-Autonomous Maximal $L^p$-Regularity for Rough Divergence Form Elliptic Operators

TL;DR

This paper establishes maximal regularity estimates in mixed Lebesgue spaces for time-dependent elliptic operators with rough spatial coefficients, advancing the understanding of their regularity properties.

Contribution

It provides the first $L^p(L^q)$ maximal regularity results for non-autonomous elliptic operators with rough spatial dependencies.

Findings

Proved $L^p(L^q)$ maximal regularity for rough divergence form operators.

Extended regularity theory to non-autonomous elliptic operators with minimal smoothness.

Established new estimates applicable to PDEs with irregular coefficients.

Abstract

We obtain $L^p(L^q)$ maximal regularity estimates for time dependent second order elliptic operators in divergence form with rough dependencies in the spatial variables.