Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 142, pp. 18.
Irregular oblique derivative problems for secondorder
nonlinear elliptic equations on infinite domains
Guo Chun Wen
Abstract:
In this article, we study irregular oblique derivative
boundaryvalue problems for nonlinear elliptic equations of
second order in an infinite domain. We first provide the formulation
of the above boundaryvalue 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 LeraySchauder 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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