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Journal of Inequalities and Applications

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Open Access 01.12.2006 | Research Article

Embedding theorems in Banach-valued -spaces and maximal -regular differential-operator equations

verfasst von: Veli B. Shakhmurov

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006

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Abstract

The embedding theorems in anisotropic Besov-Lions type spaces

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq3_HTML.gif

are studied; here

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq4_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq5_HTML.gif

are two Banach spaces. The most regular spaces

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq6_HTML.gif

are found such that the mixed differential operators

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq7_HTML.gif

are bounded from

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq8_HTML.gif

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq9_HTML.gif

, where

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq10_HTML.gif

are interpolation spaces between

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq11_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq12_HTML.gif

depending on

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq13_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq14_HTML.gif

. By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal

https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F16192/MediaObjects/13660_2004_Article_1570_IEq15_HTML.gif

-regularity of parabolic Cauchy problem are obtained. In applications, the infinite systems of the quasielliptic partial differential equations and the parabolic Cauchy problems are studied.

Vorheriger Artikel -error analysis for a system of quasivariational inequalities with noncoercive operators

Nächster Artikel The system of generalized set-valued equilibrium problems

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Titel: Embedding theorems in Banach-valued-spaces and maximal-regular differential-operator equations
verfasst von: Veli B. Shakhmurov
Publikationsdatum: 01.12.2006
Verlag: Springer International Publishing
Erschienen in: Journal of Inequalities and Applications / Ausgabe 1/2006
Elektronische ISSN: 1029-242X
DOI: https://doi.org/10.1155/JIA/2006/16192

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