Boundary Hölder gradient estimates for the Monge-Ampère equation

Abstract

We investigate global Hölder gradient estimates for solutions to the Monge-Ampère equation $$\det D^{2}u=f\mathrm{in}\Omega ,$$ where the right-hand side $f$ is bounded away from $0$ and $\infty$. We consider two main situations when a) the domain $\Omega$ is uniformly convex and b) $\Omega$ is flat.

17 pages