Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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On a solution of a nondegenerate boundary value problem of Carleman type for quasiharmonic functions in circular domains

This paper considers a Carleman type boundary value problem for quasiharmonic functions. The boundary value problem is an informal model of a Carleman type differential problem for analytic functions of a complex variable.This paper presented a complex-analytical method for solving the problem under consideration in circular domains, which makes it possible to establish the instability of its solutions concerning small contour changes.

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

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.