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.
Mots clés : Non-autonomous maximal regularity, Non-autonomous forms, Non-autonomous evolution equations, Abstract Cauchy problem
@article{AIHPC_2017__34_3_699_0, author = {Fackler, Stephan}, title = {J.-L. {Lions'} problem concerning maximal regularity of equations governed by non-autonomous forms}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {699--709}, publisher = {Elsevier}, volume = {34}, number = {3}, year = {2017}, doi = {10.1016/j.anihpc.2016.05.001}, zbl = {1375.47033}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2016.05.001/} }
TY - JOUR AU - Fackler, Stephan TI - J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 699 EP - 709 VL - 34 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2016.05.001/ DO - 10.1016/j.anihpc.2016.05.001 LA - en ID - AIHPC_2017__34_3_699_0 ER -
%0 Journal Article %A Fackler, Stephan %T J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 699-709 %V 34 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2016.05.001/ %R 10.1016/j.anihpc.2016.05.001 %G en %F AIHPC_2017__34_3_699_0
Fackler, Stephan. J.-L. Lions' problem concerning maximal regularity of equations governed by non-autonomous forms. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 699-709. doi : 10.1016/j.anihpc.2016.05.001. http://www.numdam.org/articles/10.1016/j.anihpc.2016.05.001/
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