Abstract
There are three different methods to determine harmonic Green functions for planar domains. One is based on the Schwarz boundary value problem for analytic functions. Another one is utilizing the conformal invariance of the harmonic Green function. Finally, the Schwarz reflection serves for domains the boundary of which is composed by segments of circles and lines providing a parqueting of the complex plane. Each of these methods is used exemplarily to find the harmonic Green function for particular domains.
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