J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms
Functional Analysis
2016-07-18 v2 Analysis of PDEs
Abstract
An old problem due to J.-L. Lions going back to the 1960s asks whether the abstract Cauchy problem associated to non-autonomous forms has maximal regularity if the time dependence is merely assumed to be continuous or even measurable. We give a negative answer to this question and discuss the minimal regularity needed for positive results.
Keywords
Cite
@article{arxiv.1601.08012,
title = {J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms},
author = {Stephan Fackler},
journal= {arXiv preprint arXiv:1601.08012},
year = {2016}
}
Comments
11 pages; counterexamples extended to H\"older exponent 1/2; final version