Electron. J. Diff. Equ., Vol. 2012 (2012), No. 142, pp. 1-8.

Irregular oblique derivative problems for second-order nonlinear elliptic equations on infinite domains

Guo Chun Wen

In this article, we study irregular oblique derivative boundary-value problems for nonlinear elliptic equations of second order in an infinite domain. We first provide the formulation of the above boundary-value problem and obtain a representation theorem. Then we give a priori estimates of solutions by using the reduction to absurdity and the uniqueness of solutions. Finally by the above estimates and the Leray-Schauder theorem, the existence of solutions is proved.

Submitted July 20, 2012. Published August 20, 2012.
Math Subject Classifications: 35J65, 35J25, 35J15.
Key Words: Irregular oblique derivative problem; nonlinear elliptic equations; infinite domains.

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Guo Chun Wen
LMAM, School of Mathematical Sciences
Peking University
Beijing 100871, China
email: Wengc@math.pku.edu.cn

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