Solution of Dirichlet problem for a square region in terms of elliptic functions

A broad class of steady-state physical problems can be reduced to finding the harmonic functions that satisfy certain boundary conditions. The Dirichlet problem for the Laplace ( and Poisson) equations is one of the these mentioned problems. In this study, Dirichlet problem for the Laplace (also Poisson) differential equation in a square domain is expressed in terms of elliptic functions and the solution of the problem is based on the Green function and therefore on elliptic functions. To do this, it is made use of the basic consepts associated with elliptic integrals, conform mappings and Green functions.