HAAK, Bernhard Hermann; OUHABAZ, E.-M.

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HAAK, Bernhard Hermann
Institut de Mathématiques de Bordeaux [IMB]

OUHABAZ, E.-M.
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

Mathematische Annalen. 2015p. 1-19

Springer Verlag

Résumé en anglais

We consider the maximal regularity problem for non-autonomous evolution equations of the form $u(t) + A(t) u(t) = f(t)$ with initial data $u(0) = u_0$ . Each operator $A(t)$ is associated with a sesquilinear form $a(t; *, *)$ on a Hilbert space $H$ . We assume that these forms all have the same domain and satisfy some regularity assumption with respect to t (e.g., piecewise $\alpha$-Hölder continuous for some $\alpha> 1/2$). We prove maximal Lp regularity for all initial values in the real-interpolation space $(H, D(A(0)))_{1/p,p}$ . The particular case where $p = 2$ improves previously known results and gives a positive answer to a question of J.L. Lions [11] on the set of allowed initial data $u_0$ .< Réduire

Mots clés en anglais

pseudo-differential operators

Maximal regularity

sesquilinear forms

non-autonomous evolution equations

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194443

Project ANR

Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251