Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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


For citation:

Rasulov K. M., Nagornaya T. Р. The explicit solution of the Neumann boundary value problem for Bauer differential equation in circular domains. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 3, pp. 326-335. DOI: 10.18500/1816-9791-2021-21-3-326-335

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.08.2021
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Russian
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Article type: 
Article
UDC: 
517.544.8

The explicit solution of the Neumann boundary value problem for Bauer differential equation in circular domains

Autors: 
Rasulov Karim M., Smolensk State University
Nagornaya Tatiana Романовна, Smolensk State University
Abstract: 

The article is devoted to the boundary value problem of Neumann problem's type for solutions of one second-order elliptic differential equation. Based on the general representation of the solutions of the differential equation as two analytical functions of a complex variable, and also taking into account the properties of the Schwarz equations for circles, it is established that in the case of circular domains, the boundary value problem is solved explicitly, i.e., its general solution can be found using only the F. D. Gakhov formulas for solving the scalar Riemann problem for analytic functions of a complex variable, as well as solving a finite number of linear differential equations and (or) systems of linear algebraic equations for which the matrix of the system can be written out in quadratures.

References: 
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Received: 
06.02.2021
Accepted: 
26.03.2021
Published: 
31.08.2021