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

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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 newC o-estimate and gives some new existence results. He also presents a new proof for theC 3,α-estimates of solutions, which not only weakens the smooth assumptions forF but also applies to more general nonlinear elliptic systems.

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Authors and Affiliations

  1. Department of Mathematics, Peking University, Beijing, China

    Tian Gang

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  1. Tian Gang
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Gang, T. On the existence of solutions of a class of Monge-Ampére equations. Acta Mathematica Sinica 4, 250–265 (1988). https://doi.org/10.1007/BF02560581

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  • DOI: https://doi.org/10.1007/BF02560581

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