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

摘要

In this paper, the Green function of the (interior) Dirichlet problem for the Laplace (also Poisson) differential equation in a triangle region is expressed in terms of elliptic functions and the solution of problem is based on the Green function, and therefore on elliptic functions. To do this, it is made use of the basic concepts associated with elliptic integrals, conformal mappings and Green functions. An example for the problem in the triangle region is presented as an application of the solution of Dirichlet problem. The equation is solved first by the known Method of Separation of Variables and then in terms of elliptic functions. The results of both methods are compared.