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

 Recent Issues
 The Journal Cover About the Cover Editorial Board Editors’ Interests About the Journal Scientific Advantages Submission Guidelines Submission Form Subscriptions Editorial Login Contacts Author Index To Appear ISSN: 1948-206X (e-only) ISSN: 2157-5045 (print)
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