Ukrainian Mathematical Journal

, Volume 66, Issue 7, pp 1099–1121 | Cite as

Anisotropic Differential Operators with Parameters and Applications

  • V. B. Shakhmurov

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.


Banach Space Besov Space Analytic Semigroup Fourier Multiplier Require Assertion 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • V. B. Shakhmurov
    • 1
    • 2
  1. 1.Okan UniversityIstanbulTurkey
  2. 2.Institute of Mathematics and MechanicsAzerbaijan National Academy of SciencesBakuAzerbaijan

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