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
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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