Continuous maximal regularity and analytic semigroups

Jeremy LeCrone; Gieri Simonett

Continuous maximal regularity and analytic semigroups

Analysis of PDEs 2012-09-21 v1

Authors: Jeremy LeCrone , Gieri Simonett

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

Keywords

operator semigroups operator theory on banach spaces banach algebras

Cite

@article{arxiv.1110.5690,
  title  = {Continuous maximal regularity and analytic semigroups},
  author = {Jeremy LeCrone and Gieri Simonett},
  journal= {arXiv preprint arXiv:1110.5690},
  year   = {2012}
}

Comments

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

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