Lp-solvability of parabolic problems with an operator satisfying the Kato conjecture

We study the solvability in the spaces L 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 dat...

Full description

Saved in:
Bibliographic Details
Published in:Differential equations 2015, Vol.51 (6), p.776-782
Main Author: Selitskii, A. M.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the solvability in the spaces L 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