Anisotropic differential operators with parameters and applications

In the paper, we study the boundary-value problems for parameter-dependent anisotropic differential-operator equations with variable coefficients. Several conditions for the uniform separability and Fredholmness in Banach-valued L p -spaces are given. Sharp uniform estimates for the resolvent are es...

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Bibliographic Details
Date:2014
Main Author: Shakhmurov, V.B.
Format: Article
Language:English
Published: Інститут математики НАН України 2014
Series:Український математичний журнал
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Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/166056
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Anisotropic differential operators with parameters and applications / V.B. Shakhmurov // Український математичний журнал. — 2014. — Т. 66, № 7. — С. 983–1002. — Бібліогр.: 29 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:In the paper, we study the boundary-value problems for parameter-dependent anisotropic differential-operator equations with variable coefficients. Several conditions for the uniform separability and Fredholmness in Banach-valued L p -spaces are given. Sharp uniform estimates for the resolvent are established. It follows from these estimates that the indicated operator is uniformly positive. Moreover, it is also the generator of an analytic semigroup. As an application, the maximal regularity properties of the parameter-dependent abstract parabolic problem and infinite systems of parabolic equations are established in mixed L p -spaces.