Year: 2026
Type: preprint
Abstract: We give new proofs of interior second derivative estimates for the Monge-Ampère equation and the constant quadratic Hessian equation, based on the two-point maximum principle. The arguments require only one differentiation of the equation. For the Monge-Ampère equation, the inhomogeneous term is assumed to be positive and continuously differentiable. For the quadratic Hessian equation, the estimate holds in every dimension $n\ge2$.
Source: arXiv (Cornell University)
Authors: Hung, Jui-Yun, Liu, Jiakun, Trudinger, Neil
Institutions: Australian National University, The University of Sydney
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221780101