Moscow Mathematical Journal
Volume 24, Issue 1, January–March 2024 pp. 63–89.
Free Boundary Value Problems for Abstract Elliptic Equations and Applications
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.
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
Summary:
Keywords: Free boundary value problems, differential-operator equations, Banach-valued function spaces, operator-valued multipliers, interpolation of Banach spaces, semigroup of operators.
Contents
Full-Text PDF