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Zeitschrift für Analysis und ihre Anwendungen


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Volume 27, Issue 3, 2008, pp. 301–314
DOI: 10.4171/ZAA/1356

Published online: 2008-09-30

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

Guochun Wen[1] and Zuoliang Xu[2]

(1) Peking University, Beijing, China
(2) Renmin University of China, Beijing, China

In this paper, the discontinuous irregular oblique derivative problems (or discontinuous Poincar${\rm\acute e}$ 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.

Keywords: Nonlinear elliptic equations, discontinuous irregular oblique derivative problems, complex analytic method

Wen Guochun, Xu Zuoliang: Discontinuous Irregular Oblique Derivative Problems for Nonlinear Elliptic Equations of Second Order. Z. Anal. Anwend. 27 (2008), 301-314. doi: 10.4171/ZAA/1356