Non-Autonomous Maximal Regularity for Forms Given by Elliptic Operators of Bounded Variation

TL;DR

This paper establishes maximal regularity results for non-autonomous elliptic operators with bounded variation in time, extending the theory to a broad class of operators with measurable coefficients.

Contribution

It proves maximal L^p-regularity for non-autonomous elliptic operators with bounded variation, including cases with measurable coefficients, under trace space stability conditions.

Findings

Maximal L^p-regularity holds for p in (1,2] on L^2.

Results apply to elliptic operators with measurable coefficients.

Provides a framework for non-autonomous problems with bounded variation.

Abstract

We show maximal $L^p$-regularity for non-autonomous Cauchy problems provided the trace spaces are stable in some parameterized sense and the time dependence is of bounded variation. In particular, on $L^2$, we obtain for all $p \in (1,2]$ maximal $L^p$-regularity for non-autonomous elliptic operators with measurable coefficients.