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

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.

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Publication Details

Journal
Izvestiya of Saratov University Mathematics Mechanics Informatics
Published
2025-02-21
DOI
https://doi.org/10.18500/1816-9791-2025-25-1-46-52
Primary Topic
Advanced Mathematical Modeling in Engineering
Type
article
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article

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

К. М. Расулов, Tatiana Романовна Nagornaya
Izvestiya of Saratov University Mathematics Mechanics Informatics
Advanced Mathematical Modeling in Engineering
article

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

К. М. Расулов, Tatiana Романовна Nagornaya
article en

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.

Izvestiya of Saratov University Mathematics Mechanics InformaticsVol. 25(1)
Openalex Percentile: Top 95%
Advanced Mathematical Modeling in Engineering
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