Vol. 9, No. 6, 2016

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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 C2 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
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