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Moscow Mathematical Journal

Volume 24, Issue 1, January–March 2024  pp. 63–89.

Free Boundary Value Problems for Abstract Elliptic Equations and Applications

Authors:  Veli B. Shakhmurov (1)
Author institution:(1) Antalya Bilim University Department of Industrial Engineering, Dosemealti, 07190 Antalya, Turkey
Azerbaijan State Economic University, Center of analytical-information resource 194 M. Mukhtarov AZ1001 Baku, Azerbaican
Western Caspian University, Physics and Technical Sciences, 31, Istiglaliyyat Street, Baku, Azerbaican


Free boundary value problem for abstract elliptic equations with variable coefficients is studied. The equations involve linear operators in Banach space $E$. The uniform maximal regularity properties and Fredholmness of this problem are obtained in $E$-valued Hölder spaces. 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 are established.

2020 Math. Subj. Class. 35xx, 47Fxx, 47Hxx, 35Pxx.

Keywords: Free boundary value problems, differential-operator equations, Banach-valued function spaces, operator-valued multipliers, interpolation of Banach spaces, semigroup of operators.

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