Integral problem for abstract elliptic equations and applications
Complex Variables and Elliptic Equations, vol.71, no.7, pp.1479-1504, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 71 Issue: 7
- Publication Date: 2026
- Doi Number: 10.1080/17476933.2025.2543398
- Journal Name: Complex Variables and Elliptic Equations
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
- Page Numbers: pp.1479-1504
- Keywords: Banach-valued function spaces, Differential-operator equations, interpolation of Banach spaces, Nonlocal boundary value problems, operator-valued multipliers, semigroup of operators
- Open Archive Collection: Article
- Azerbaijan State University of Economics (UNEC) Affiliated: Yes
Abstract
Integral boundary value problem for abstract elliptic equation with variable coefficients is studied. The uniform maximal regularity properties and Fredholmness of this problem are obtained in vector-valued (Formula presented.) -spaces. It is proven that the corresponding differential operator is positive and is a generator of an analytic semigroup. Then we derive the existence and uniqueness of the solution for the nonlinear elliptic problem. In application, the maximal regularity properties of Cauchy problem for abstract parabolic equation and anisotropic elliptic equations are established.