Mixed problem for the Laplace equation outside cuts in a plane with setting Dirichlet and skew derivative conditions on the different sides of the cuts

The mixed problem for the Laplace equation outside cuts in a plane is considered. The Dirichlet condition is posed on one side of each cut and the skew derivative condition is posed on the other side. This problem generalizes the mixed Dirichlet-Neumann problem. By using the method of potential, the problem is reduced to the uniquely solvable Fredholm equation of the 2nd type.