The 2-Dimensional Dirichiet Problem in an External Domain with Cuts

Abstract

The Dirichlet problem for the Laplace equation in an external connected plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredhoim equation of the second kind, which is uniquely solvable. Consequently, the solution can be computed by standard codes. The solvability of the Dirichlet problem in an internal domain with cuts is proved with the help of a conformal mapping.