Discontinuous Irregular Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order

Abstract

In this paper, the discontinuous irregular oblique derivative problems (or discontinuous Poincar$\acute{\mathrm{e}}$ boundary value problems) for nonlinear elliptic equations of second order in multiply connected domains are discussed by using a complex 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 result about the continuous irregular oblique derivative problem for the nonlinear equations is derived.