Asymptotic behavior at infinity of solutions of Monge-Ampère equations in half spaces

Xiaobiao Jia, Dongsheng Li, Zhisu Li

We prove that any convex viscosity solution of $\det D^{2}u=1$ outside a bounded domain of ${\mathbb{R}}_{+}^n$ tends to a quadratic polynomial at infinity with rate at least $\frac{x_n…