The oblique derivative problem for nonlinear elliptic equations of second order in unbounded domains

被引：0

作者：

Wen, Guochun ^{[1
]}

Xu, Zuoliang ^{[2
]}

机构：

[1] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[2] Renmin Univ China, Sch Informat, Beijing 100872, Peoples R China

来源：

MATHEMATICAL SCIENCES | 2012年 / 6卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Oblique derivative problem; Nonlinear elliptic equations; Unbounded domains;

D O I：

10.1186/2251-7456-6-57

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article deals with the general oblique derivative boundary value problem for nonlinear elliptic equations of second order in an unbounded multiply connected domain. The problem includes the Dirichlet problem, the Neumann problem and the third boundary value problem as its spacial cases. We first provide the formulation of the above boundary value problem and obtain the representation theorem for the problem. Then, we give a priori estimates of solutions for the boundary value problem by using the reduction to absurdity and the uniqueness of solutions. Finally, by the above estimates of solutions and the Leray-Schauder theorem, the existence of solutions of the above problem for the nonlinear elliptic equations of second order can be proved.

引用

页数：7