#### Vol. 9, No. 6, 2016

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The interior $C^2$ estimate for the Monge–Ampère equation in dimension $n=2$

### Chuanqiang Chen, Fei Han and Qianzhong Ou

Vol. 9 (2016), No. 6, 1419–1432
##### Abstract

We introduce a new auxiliary function, and establish the interior ${C}^{2}$ estimate for the Monge–Ampère equation in dimension $n=2$, which was first proved by Heinz by a geometric method.

##### Keywords
interior $C^2$ a priori estimate, Monge–Ampère equation, $\sigma_2$ Hessian equation, optimal concavity
##### Mathematical Subject Classification 2010
Primary: 35B45, 35B65, 35J96