Non-autonomous right and left multiplicative perturbations and maximal regularity

Abstract

We consider the problem of maximal regularity for non-autonomous Cauchy problems $u^{\prime }(t)+B(t)A(t)u(t)+P(t)u(t)=f(t),u(0)=u_0$ and $u^{\prime }(t)+A(t)B(t)u(t)+P(t)u(t)=f(t),u(0)=u_0$. In both cases, the time dependent operators $A(t)$ are associated with a family of sesquilinear forms and the multiplicative left or right perturbations $B(t)$ as well as the additive perturbation $P(t)$ are families of bounded operators on the considered Hilbert space. We prove maximal $L_p$-regularity results and other regularity properties for the solutions of the previous problems under minimal regularity assumptions on the forms and perturbations.

Cited by in corpus (1)

• J. L. Lions' Problem on Maximal Regularity