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
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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