数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 950-963.

• 论文 • 上一篇    下一篇

退化的Monge-Ampére方程解的C1,1先验估计

李书选1,2|邓晶1   

  1. 1.中国科学院武汉物理与数学研究所 武汉 430071|2.南阳师范学院数学与统计学院 河南 南阳 473061
  • 收稿日期:2010-12-16 修回日期:2012-05-10 出版日期:2012-10-25 发布日期:2012-10-25
  • 基金资助:

    国家自然科学基金(10901159)和南阳师范学院专项项目(ZX2012019)资助

C1,1 a Priori Estimates for the Degenerate Monge-Ampére Equation

 LI Shu-Xuan1,2, DENG Jing1   

  1. 1.Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071|2.School of Mathematics and Statistics, Nanyang Normal University, Henan Nanyang 473061
  • Received:2010-12-16 Revised:2012-05-10 Online:2012-10-25 Published:2012-10-25
  • Supported by:

    国家自然科学基金(10901159)和南阳师范学院专项项目(ZX2012019)资助

摘要:

研究退化的Monge-Ampére方程
{det D2u=f(x, u, Du)     in Ω,
 u=φ                               on ∂Ω.
的Dirichlet问题. 推广文献[6]的结果至一般情形, 并对在文献[6]中关键的法向导数的估计做出改进, 使其更明显地不依赖于方程的解本身.

关键词: Monge-Ampére方程, 退化, C1,1先验估计

Abstract:

In this paper, we study the Dirichlet problem for the degenerate Monge-Ampére equation

{det D2u=f(x, u, Du)     in Ω,
 u=φ                               on ∂Ω.
We generalize [6] to the general case, make a modification on the proof of the estimates for normal derivative, which is crucial in [6], and then make the independence of the estimate on the solutions themselves more obviously.

Key words: Monge-Ampére equation, Degenerate, C1,1 a priori estimate

中图分类号: 

  • 35J60