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 · 2025
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.