Interior second derivative estimates for solutions to the linearized Monge--Ampère equation

Cristian E. Gutiérrez, Truyen Nguyen

Let $\Omega \subset {\mathbb{R}}^n$ be a bounded convex domain and $\varphi \in C(\bar{\Omega })$ be a convex function such that $\varphi$ is sufficiently smooth on $\partial \Omega$ and the Monge--Ampère measure $\det D^2ϕ…