| Abstract: | The question of the existence and uniqueness of the solutions of the system  in case of rotational symmetry can be reduced to the question of the resolvibility of a nonlinear elliptic differential equation for α which contains an arbitrary function g(α). Under rather general suppositions the boundary values of α and the function g(α) are given by the boundary values of H⊥ and H φ (the component of H which is perpendicular to the boundary). From the theory of non-linear elliptic equations one obtains: In sufficiently small domains the boundary value problem has a unique solution. For large domains these exist estimations about the diameter and area which guarantee the existence and uniqueness of the solutions. |
