Maximal regularity for non-autonomous Cauchy problems in weighted spaces

Abstract

We consider the regularity for the non-autonomous Cauchy problem $$ u'(t) + A(t) u(t) = f(t)\quad (t \in [0, \tau]), \quad u(0) = u_0. $$ The time dependent operator A(t) is associated with (time dependent) sesquilinear forms on a Hilbert space \(\mathcal{H}\). We prove the maximal regularity result in temporally weighted L^2-spaces and other regularity properties for the solution of the problem under minimal regularity assumptions on the forms and the initial value u_0. Our results are motivated by boundary value problems.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/124/abstr.html