In this paper, the discontinuous irregular oblique derivative problems (or discontinuous Poincar 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.
Cite this article
Guochun Wen, Zuoliang Xu, Discontinuous Irregular Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order. Z. Anal. Anwend. 27 (2008), no. 3, pp. 301–314DOI 10.4171/ZAA/1356