Mixed problem in a magnetized semiconductor film with cuts along a straight line

The boundary value problem for harmonic functions is considered in the exterior of straight line cuts in a plane. The Dirichlet boundary condition is specified on one side of each cut and the skew derivative boundary condition is specified on the other side of each cut. The explicit solution of the problem is obtained with the help of the theory of analytic complex functions. Uniqueness of the solution is proved. The problem describes electric current from straight line electrodes in a semiconductor film placed in a constant magnetic field.