Global Monge-Ampere equation with asymptotically periodic data

Abstract

Let $u$ be a convex solution to $\det (D^{2}u)=f$ in ${\mathbb{R}}^n$ where $f\in C^{1,\alpha }({\mathbb{R}}^n)$ is asymptotically close to a periodic function $f_p$. We prove that the difference between $u$ and a parabola is asymptotically close to a periodic function at infinity, for dimension $n\ge 3$.

20 pages

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