The interior \(C^2\) estimate for the Monge-Ampère equation in dimension \(n = 2\)
The paper deals with convex solutions of the Monge-Ampère equation NEWLINE\[NEWLINE\det D^2u=f(x)\quad \text{in }B_R(0)\subset\mathbb R^2.NEWLINE\]NEWLINE The interior \(C^2\) estimates for the convex solutions have been proved by \textit{E. Heinz} [J. Anal. Math. 7, 1--52 (1959; Zbl 0152.30901)] for planar planar domains, and by \textit{A. V. Pogorelov} [The Minkowski multidimensional problem. New York etc.: John Wiley \& Sons (1978; Zbl 0387.53023)] for dimensions \(n\geq3\).NEWLINENEWLINEThe authors rediscover the Heinz result by considering suitable new auxiliary functions.
scientific article; zbMATH DE number 6637201