Mixed boundary problem of magnetized semiconductor physics in an external domain

The authors consider a mixed problem for the Laplace equation in an external multiply connected domain with a boundary composed of simple closed curves. The Dirichlet condition is preset on some curves and a condition with the skew derivative on the other curves. The problem is reduced to the uniquely solvable Fredholm equation of the second kind in the space of continuous functions. The existence and uniqueness of the solution are proved.