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arXiv · 1406.1386

Global Monge-Ampere equation with asymptotically periodic data

Eduardo V. Teixeira·Lei Zhang
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Abstract

Let $u$ be a convex solution to $\det(D^2u)=f$ 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 $n\ge 3$.

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Eduardo V. Teixeira, Lei Zhang. 2014-06-05. Global Monge-Ampere equation with asymptotically periodic data. https://arxiv.org/abs/1406.1386

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