Method of angular potential in the boundary value problems of magnetised semiconductors physics

The skew derivative problem and the mixed problem for the Laplace equation in an multiply connected domain is solved. These problems describe electric current in semiconductors placed in a homogeneous magnetic field. The normal current density and the potential is specified at the boundary. The existence and uniqueness of a solution are studied. The skew derivative problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. The same result is obtained for the mixed problem.