On the existence of solutions of a class of Monge-Ampére equations

Gang Tian

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

In this paper, the Dirichlet problem for the Monge-Ampére equation det(u ij)=F(x,u,Δu) on a convex bounded domain ΩσR″ is considered. The author establishes a new C o-estimate and gives some new existence results. He also presents a new proof for the C 3,α-estimates of solutions, which not only weakens the smooth assumptions for F but also applies to more general nonlinear elliptic systems.

Original languageEnglish (US)
Pages (from-to)250-265
Number of pages16
JournalActa Mathematica Sinica
Volume4
Issue number3
DOIs
StatePublished - Sep 1 1988

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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