On the electron plasma dynamics in the magnetized semiconductor film with the electrode placed at the arc of a circumference

The explicit solution of the boundary value problem for harmonic functions is constructed in the exterior of a cut in a plane. The skew derivative boundary condition is specified at the cut placed along a circumference. The problem describes the dynamics of the electron plasma in the magnetized semiconductor film with the electrode placed at the arc of a circumference. The problem is solved by reduction to the Riemann–Hilbert problem for analitic complex functions. The solution of the Riemann–Hilbert problem is obtained explicitly.