On the admissibility of observation operators in the context of maximal regularity

Abstract

We study admissible observation operators for perturbed evolution equations using the concept of maximal regularity. We first show the invariance of the maximal $L^p$-regularity under non-autonomous Miyadera-Voigt perturbations. Second, we establish the invariance of admissibility of observation operators under such a class of perturbations. Finally, we illustrate our result with two examples, one on a non-autonomous parabolic system, and the other on an evolution equation with mixed boundary conditions and a non-local perturbation.