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

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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Correspondence to Veli B. Shakhmurov.

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Shakhmurov, V.B. Embedding theorems in Banach-valued-spaces and maximal-regular differential-operator equations. J Inequal Appl 2006, 16192 (2006). https://doi.org/10.1155/JIA/2006/16192

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Keywords

  • Differential Equation
  • Banach Space
  • Partial Differential Equation
  • Cauchy Problem
  • Differential Operator
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