On a boundary value problem, describing the Hall effect in a semi-conductor with two periodic sets of electrodes

We construct the explicit solution of the boundary value problem on the electric flow from periodic electrodes in a semiconductor film placed in a constant magnetic field. Electrodes form two periodic systems in a semiconductor. From the mathematical point of view we study boundary value problem for harmonic functions outside straight-line periodic cuts in a plane. The skew derivative boundary condition is specified on the cuts.