Continuous maximal regularity and analytic semigroups

Jeremy LeCrone; Gieri Simonett

doi:10.3934/proc.2011.2011.963

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2011, Volume 2011: 963-970. Doi: 10.3934/proc.2011.2011.963 open access

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Continuous maximal regularity and analytic semigroups

Jeremy LeCrone^1, and
Gieri Simonett^1,

1.
Department of Mathematics, Vanderbilt University, Nashville, TN 37240

Received: June 30, 2010

Revised: February 28, 2011

Published: August 2017

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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 $E_1$.

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Mathematics Subject Classification: Primary: 35K90, 47D06; Secondary: 35K35.

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