数学物理学报(英文版)

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SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC#br# EQUATIONS OF SECOND ORDER

闻国椿   

  1. 北京大学数学学院, 北京 100871
  • 收稿日期:2004-03-08 修回日期:2005-12-02 出版日期:2007-07-20 发布日期:2007-07-20
  • 通讯作者: 闻国椿
  • 基金资助:

    This research is supported by NSFC (10671207).

SOME BOUNDARY VALUE PROBLEMS FOR NONLINEAR DEGENERATE ELLIPTIC#br# EQUATIONS OF SECOND ORDER

Wen Guochun   

  1. School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2004-03-08 Revised:2005-12-02 Online:2007-07-20 Published:2007-07-20
  • Contact: Wen Guochun

摘要:

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above
problem is proved. In this article, the complex analytic method
is used, namely the corresponding problem for degenerate elliptic
complex equations of first order is firstly discussed, afterwards
the above problem for the degenerate elliptic equations of second
order is solved.

关键词: Boundary value problems, nonlinear elliptic equations, parabolic degeneracy

Abstract:

The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem. Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension, the existence of solutions of the above
problem is proved. In this article, the complex analytic method
is used, namely the corresponding problem for degenerate elliptic
complex equations of first order is firstly discussed, afterwards
the above problem for the degenerate elliptic equations of second
order is solved.

Key words: Boundary value problems, nonlinear elliptic equations, parabolic degeneracy

中图分类号: 

  • 35J25