Continuous maximal regularity and analytic semigroups

Details Continuous maximal regularity and analytic semigroups Continuous maximal regularity and analytic semigroups

2011-10-26

arxiv.org/abs/1110.5690v1

Mathematics

Analysis of PDEs

8 pages, To appear in Dynamical Systems and Differential Equations, DCDS Supplement 2011: Proceedings of the 8th AIMS Internat

Scientific paper

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 $A: E_1 \rightarrow E_0$ implies that $A$ generates a strongly continuous analytic semigroup on $E_0$ with domain equal $E_1$.

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