Maximal regularity for non-autonomous evolution equations
Language
en
Article de revue
This item was published in
Mathematische Annalen. 2015p. 1-19
Springer Verlag
English Abstract
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; *, ...Read more >
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 $u_0$ .Read less <
English Keywords
pseudo-differential operators
Maximal regularity
sesquilinear forms
non-autonomous evolution equations
ANR Project
Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013
Origin
Hal imported