The Basic Boundary Problem of Magnetized Semiconductors Physics

The skew derivative problem for the Laplace equation in an interior multiply connected domain is solved. This problem describes electric current in semiconductors placed in a homogeneous magnetic field. The existence and uniqueness of a solution are studied. The problem is reduced to a Fredholm equation of the second kind, which is uniquely solvable. The same result is obtained for the problem in an exterior multiply connected domain with the three different conditions at infinity. It is shown that the existence and uniqueness of a solution depend on the condition at infinity.