The Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cutsThe Dirichlet problem for the two-dimensional Laplace equation in a multiply connected domain with cuts
Proceedings of the Edinburgh Mathematical Society (Series 2)
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.