English

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