Maximal regularity of the abstract Cauchy problem

Abstract

In this thesis we will study maximal regularity of the abstract Cauchy problem while introducing the notion of strict maximal regularity, which also requires the solution to be p-th power integrable. We will study relations between these two notions of maximal regularity and see that they are strongly linked to analytic semigroups. Furthermore, we will show that (strict) maximal regularity is independent of the power p and prove sufficient conditions if the underlying space happens to be a Hilbert space.