RIEMANN-HILBERT BOUNDARY VALUE PROBLEMS FOR IMPROPERLY ELLIPTIC EQUATIONS IN THE EXTERIOR OF A DISC

摘要

The paper studies the Riemann-Hilbert problem for improperly elliptic equations in the exterior of the unit disc. The solutions are found in the class of functions that are bounded in the neighborhood of infinity and satisfy Holder's condition in any finite part of the disc exterior, up to its boundary. Some conditions for unique solvability of the problem in question are obtained and an effective solution method is presented. The same methods also work in the Poincare problem for improperly elliptic equations in the exterior of the disc.