Open Access

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

Journal of Inequalities and Applications20062006:16192

DOI: 10.1155/JIA/2006/16192

Received: 28 September 2004

Accepted: 4 May 2006

Published: 31 July 2006

Abstract

The embedding theorems in anisotropic Besov-Lions type spaces are studied; here and are two Banach spaces. The most regular spaces are found such that the mixed differential operators are bounded from to , where are interpolation spaces between and depending on and . By using these results the separability of anisotropic differential-operator equations with dependent coefficients in principal part and the maximal -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.

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Authors’ Affiliations

(1)
Department of Electrical & Electronics Engineering, Engineering Faculty, Istanbul University

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© Shakhmurov 2006

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