Browsing by Author "Shakhmurov, V. B."

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    SINGULAR PERTURBATIONS FOR ABSTRACT ELLIPTIC OPERATORS AND APPLICATIONS
    (Turkic World Mathematical Soc, 2012) Shakhmurov, V. B.
    Dirichlet problem for parameter depended elliptic differential-operator equation with variable coefficients in smooth domains is studied. The uniform maximal regularity, Fredholmness and the positivity of this problem in vector-valued Lp-spaces are obtained. It is proven that the corresponding differential operator is positive and is a generator of an analytic semigroup. In application, the maximal regularity properties of Cauchy problem for abstract parabolic equation and anisotropic elliptic equations with small parameters are established.