Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts

P. A. Krutitskiia1

a1 Department of Mathematics, Faculty of Physics, Moscow State University, Moscow 119899, Russia


The Dirichlet problem for the Laplace equation in a connected-plane region with cuts is studied. The existence of a classical solution is proved by potential theory. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable.

(Received April 29 1998)


  • Laplace equation;
  • Dirichlet problem;
  • cracked adomain