Asymptotic expansion at infinity of solutions to Monge-Ampère equation with $C^α$ right term

Abstract

We develop a non-local method to establish the asymptotic expansion at infinity of solutions to Monge-Ampère equation $\det(D^2v)=f$ on $\rn$, where $f$ is a perturbation of $1$ and is only assumed to be Hölder continuous outside a bounded subset of $\rn$, compared to the previous work that $f$ is at least $C^2$.