J. L. Lions' Problem on Maximal Regularity

TL;DR

This survey reviews recent advances in maximal regularity for non-autonomous equations on Hilbert spaces and presents new results illustrating the theory's limitations.

Contribution

It provides a comprehensive overview of recent progress and introduces two new results that demonstrate the boundaries of current maximal regularity theory.

Findings

Summarizes recent progress in maximal regularity theory.

Introduces two new results showing the limits of the theory.

Abstract

This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It also contains two new results showing the limits of the theory.