A theorem of the Dore-Venni type for noncommuting operators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A theorem of the Dore-Venni type for noncommuting operators

Authors:	Sylvie Monniaux Jan Prü ss

Institution:	Mathematik V, Universität Ulm, D-89069 Ulm, Germany ; Fachbereich Mathematik und Informatik, Martin-Luther- Universität Halle-Wittenberg, Theodor-Lieser-Str. 5, D-06120 Halle, Germany

Abstract:	A theorem of the Dore-Venni type for the sum of two closed linear operators is proved, where the operators are noncommuting but instead satisfy a certain commutator condition. This result is then applied to obtain optimal regularity results for parabolic evolution equations $\dot{u}(t)+L(t)u(t)=f(t)$ and evolutionary integral equations $u(t)+\int _0^ta(t-s)L(s)u(s)ds = g(t)$ which are nonautonomous. The domains of the involved operators may depend on , but $L(t)^{-1}$ is required to satisfy a certain smoothness property. The results are then applied to parabolic partial differential and integro-differential equations.

Keywords:	Sum of linear operators bounded imaginary powers of linear operators commutator conditions parabolic evolution equations parabolic evolutionary integral equations completely positive kernels fractional derivatives creep functions viscoelasticity

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