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

Tian Gang

doi:10.1007/BF02560581

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

Tian Gang

Mathematics

Research output: Contribution to journal › Article › peer-review

24 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 language	English (US)
Pages (from-to)	250-265
Number of pages	16
Journal	Acta Mathematica Sinica
Volume	4
Issue number	3
DOIs	https://doi.org/10.1007/BF02560581
State	Published - Sep 1988

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF02560581

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abstract = "In this paper, the Dirichlet problem for the Monge-Amp{\'e}re 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.",

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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