HOMOGENEOUS RIEMANN BOUN DARY VALUE PROBLEM WITH MEROMORPHIC COEFFICIEN TS FOR INFINITELY CONNECTED DOMAIN
Abstract
Homogeneous Riemann boundary value problem with meromorphic coefficients for infinitely connected domains is considered. In the closed form the problem is solved in the class of piece-wise analytic functions, possessing meromorphic continuation to the whole complex plane. Special attention is paid to the existence of doubly periodic solutions to the problem with elliptic coefficients. The example of the problem having a unique solution up to an arbitrary constant multiplier is presented, as well as of the problem with a solution depending on a number of arbitrary parameters. The obtained results can be used for solving of an inhomogeneous Riemann boundary value problem with meromorphic coefficients in an infinitely connected domain in the general statement.
About the Author
M. M. Yukhimuk
Brest State Technical University
Belarus
Senior Lecturer of the Department of Higher Mathematics
Belarus
Senior Lecturer of the Department of Higher Mathematics
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