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Continuous maximal regularity and analytic semigroups

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  • 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 $E_1$.
    Mathematics Subject Classification: Primary: 35K90, 47D06; Secondary: 35K35.


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