Asymptotic expansion at infinity of solutions to Monge-Ampère equation with Cα right term

Abstract

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