L^sub p^-solvability of parabolic problems with an operator satisfying the Kato conjecture

We study the solvability in the spaces L ^sup p^(0, T;X) of an abstract parabolic equation with an operator defined by a sesquilinear form satisfying the Kato conjecture, where X is a Hilbert space obtained by interpolation between the domain of the form and the dual space. We describe the initial d...

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Bibliographic Details
Published in:Differential equations 2015-06, Vol.51 (6), p.776
Main Author: Selitskii, A M
Format: Article
Language:English
Subjects:
Differential equations
Hilbert space
Mathematical analysis
Partial differential equations
Studies
Online Access:Get full text
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Summary:We study the solvability in the spaces L ^sup p^(0, T;X) of an abstract parabolic equation with an operator defined by a sesquilinear form satisfying the Kato conjecture, where X is a Hilbert space obtained by interpolation between the domain of the form and the dual space. We describe the initial data spaces for various values of p and show that in the most common cases they coincide with the Besov spaces.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266115060087