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

Fackler, Stephan

doi:10.1016/j.anihpc.2016.05.001

Fackler, Stephan

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 3, pp. 699-709.

Résumé

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.

Zbl

DOI : 10.1016/j.anihpc.2016.05.001

Classification : 35B65, 47A07
Mots clés : Non-autonomous maximal regularity, Non-autonomous forms, Non-autonomous evolution equations, Abstract Cauchy problem

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     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/}
}

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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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