Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (5): 950-963.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 35J60
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