Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Rasulov K. M., Nagornaya T. R. A method for solving the Poincare boundary value problem for generalized harmonic functions in circular domains. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 1, pp. 46-52. DOI: 10.18500/1816-9791-2025-25-1-46-52, EDN: HZNJHM

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.02.2025
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Russian
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Article
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517.544.8
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HZNJHM

A method for solving the Poincare boundary value problem for generalized harmonic functions in circular domains

Autors: 
Rasulov Karim M., Smolensk State University
Nagornaya Tatyana Romanovna, Smolensk State University
Abstract: 

The paper considers a Poincare-type boundary value problem for a second-order elliptic differential equation that generates a class of generalized harmonic functions. It is established that in the case of circular domains the solution of the considered boundary value problem reduces to the solution of a Riemann-type differential boundary value problem in the classes of analytic functions of a complex variable. In addition, necessary and sufficient conditions for the solvability of the problem are obtained.

References: 
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Received: 
21.06.2023
Accepted: 
23.07.2023
Published: 
28.02.2025