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A mixed problem with a Dirichlet-Neumann boundary condition in the first quadrant for the Poisson equation

Abstract:

In this article the Dirichlet-Neumann mixed problem for the Poisson equation in the first quadrant is solved. The method of the reflections of the complex plane is used to construct a Green function that allows or solves the problem. The solution is presented in the form of an integral operator and some applications are shown to inductance and capacitance problems in the electrical lines, phenomenal heat in bodies of large dimensions, mechanical water solids-fluids, electromagnetism. The results presented serve as a model for other mixed problems of the Poisson equation in other non-bounded domains gene-rando other mathematical models that can be applied.