The interior $C^2$ estimate for Monge-Ampere equation in dimension $n=2$

preprint2016arXivOpen access

In this paper, we introduce a new auxiliary function, and establish the interior $C^2$ estimate for Monge-Ampere equation in dimension $n =2$ , which was firstly proved by Heinz \cite{H59}.

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The interior $C^2$ estimate for Monge-Ampere equation in dimension $n=2$

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The interior C2C^2C2 estimate for Monge-Ampere equation in dimension n=2n=2n=2

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The interior $C^2$ estimate for Monge-Ampere equation in dimension $n=2$