J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms
Stephan Fackler · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2016
An old problem due to J.-L. Lions going back to the 1960s asks whether the abstract Cauchy problem associated to non-autonomous symmetric 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.