Discontinuous irregular oblique derivative problems for nonlinear elliptic equations of second order

In this paper, the discontinuous irrregular oblique derivative problems (or discontinuous Poincare boundary value problems) for nonlinear elliptic equaitons of second order in multiply connected domains are discussed by using a comples analytic method. Firstly the uniqueness of solutions for such boundary value problems is proved and a priori estimates of their solutions are given, and then by the Leray-Schauder theorem, the existence of solutions of the above problems is verified. As a special case the resutl about the continuous irregular oblique derivative problem for the nonliear equations is derived.