The interior $C^2$ estimate for Monge-Ampere equation in dimension $n=2$

TL;DR

This paper presents a new auxiliary function to establish interior $C^2$ estimates for the Monge-Ampere equation specifically in two dimensions, building on Heinz's foundational work.

Contribution

The paper introduces a novel auxiliary function to prove interior $C^2$ estimates for the Monge-Ampere equation in two dimensions, providing an alternative approach to Heinz's original proof.

Findings

Established interior $C^2$ estimate in 2D for Monge-Ampere equation

Introduced a new auxiliary function for the proof

Extended the understanding of regularity in Monge-Ampere equations

Abstract

In this paper, we introduce a new auxiliary function, and establish the interior $C^2$ estimate for Monge-Ampere equation in dimension $n =2$, which was firstly proved by Heinz \cite{H59}.