J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms

  • Stephan Fackler

    Institute of Applied Analysis, University of Ulm, Helmholtzstr. 18, 89069 Ulm, Germany

Abstract

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.

Cite this article

Stephan Fackler, J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 699–709

DOI 10.1016/J.ANIHPC.2016.05.001