Continuous maximal regularity and analytic semigroups

Jeremy LeCrone; Gieri Simonett

paper

Continuous maximal regularity and analytic semigroups

arXiv:1110.5690

Abstract

In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity for a closed operator $A : E_{1} \to E_{0}$ implies that $A$ generates a strongly continuous analytic semigroup on $E_{0}$ with domain equal $E_{1}$ .

arXiv comment8 pages, To appear in Dynamical Systems and Differential Equations, DCDS Supplement 2011: Proceedings of the 8th AIMS International Conference (Dresden, Germany)