J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous Forms

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.

11 pages; counterexamples extended to Hölder exponent 1/2; final version

References in corpus (1)

• Non-Autonomous Maximal Regularity in Hilbert Spaces

Cited by in corpus (9)

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• Ultracontractivity and Gaussian bounds for evolution families associated with non-autonomous forms
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• Maximal regularity for generalized boundary conditions in time
• J. L. Lions' Problem on Maximal Regularity
• Stability for evolution equations governed by a non-autonomous form
• On the norm-continuity for evolution family arising from non-autonomous forms