Bulletin of Computational Applied Mathematics (Bull CompAMa)
A fundamental solution for the Laplace operator in a doubly connected domain
Jose Luis Vergara Ibarra, Carmen Judith Vanegas
In this work, we find a harmonic Green function for a doubly connected domain using the theory of conformal mappings and then we define a Poisson kernel. Using these functions an integral representation formula for the solution of the Dirichlet problem for the Poisson equation is derived.
Keywords: Harmonic Green functions; multiply connected domain; conformal invariance.