Green's function on an infinite horizontal strip of amplitude π with Dirichlet-Neumann mixed frontier using the parqueting-reflections method

Abstract

This article deals with the construction of a Green harmonic function in a domain consisting of an infinite horizontal band in ℂ of amplitude π whose bounded is mixed under the Dirichlet-Neumann conditions, such a function will be generated using analytical processes based on the method of reflections. The ideas produced in this research can be used in other types of mixed problems and other partial differential equations whose domains are delimited or not. The Green function generated allows obtaining the Poisson Kernel, which leads to the production of integral representations of solutions of boundary value problems in partial differential equation.