|
|||||
 |
|
|
|
|
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 estimate for the Monge–Ampère equation in dimension , 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
|
Milestones
Received: 29 September 2015
Revised: 28 December 2015
Accepted: 12 May 2016
Published: 3 October 2016
|
Authors |
| Chuanqiang Chen | |
| Department of Applied
Mathematics Zhejiang University of Technology No. 288, Liuhe Road Xihu District Hangzhou, 310023 Zhejiang Province China |
|
| Fei Han | |
| School of Mathematics Sciences Xinjiang Normal University No. 102, Xinyi Road Shayibake District Urumqi, 830054 Xinjiang Uygur Autonomous Region China |
|
| Qianzhong Ou | |
| School of Science Hezhou University No. 18, Xihuan Road Hezhou, 542899 Guangxi Province China |
|
|
