Monge-Ampere equation on exterior domains

Jiguang Bao, Haigang Li, Lei Zhang

We consider the Monge-Ampère equation $\det (D^{2}u)=f$ where $f$ is a positive function in ${\mathbb{R}}^n$ and $f=1+O(|x{|}^{-\beta })$ for some $\beta >2$ at infinity. If the equation is globally…