On oblique derivative problem for a plane with sections along the straight line and relating problems

The research method of the mathematical problem arising in the description of the electric current through the magnetized semiconductor according to the model, suggested by S. A. Gabov and P. A. Krutitsky (Mat. mod., 1989, v. 1, № 5, pp. 71–79) is given. From the mathematical point of view the question about equivalence oblique derivative problem at the plane with sections along the straight line for harmonic functions and corresponding Riemarm–Hilbert problem is studied. The enough general case, for which Riemann–Hilbert problem and the oblique derivative problem can be solved in explicit form, is considered.