On the theory of generalized analytic Vekua functions with a singular point
Otelbaev M. Koshanov B.D. Oralbekova N.O.
2025Taylor and Francis Ltd.
Complex Variables and Elliptic Equations
2025#70Issue 71254 - 1272 pp.
This work consists of two sections. The first section examines the elliptic system of equations (Formula presented.) The concept of Vekua spaces (V-spaces) is introduced, namely: a Banach function space B is a Vekua space if the theorem about continuity of the solution of an inhomogeneous equation and the theorem about the representation of solutions of a homogeneous equation holds for any functions (Formula presented.) and (Formula presented.). The following main statement is obtained (Theorem 7.1): A function space B possessing the properties (Formula presented.) of § 2 is a V–space if and only if (Formula presented.) (for the definition of (Formula presented.) see § 2). From this result it follows that a symmetric space is a V space if and only if it is continuously embedded in the Lorentz space (Formula presented.) (Theorem 7.3). Thus, we can say that the widest space to which the Vekua theory can be extended is (Formula presented.), and among all symmetric spaces - (Formula presented.). In the second section, we study the following equation with singular point (Formula presented.) The paper proves the existence of solutions to this equation in the functional class B introduced in the first part of the article. Representations of the 1st and 2nd types of solutions from this class are obtained.
boundary value problem , continuity of solution , First order elliptic system , integral representations of solution , polyharmonic equation
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
International University of Information Technologies, Almaty, Kazakhstan
D. Serikbayev East Kazakhstan Technical University, Oskemen, Kazakhstan
Institute of Mathematics and Mathematical Modeling
International University of Information Technologies
D. Serikbayev East Kazakhstan Technical University
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