Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior at infinity of solutions of Monge-Amp\`ere equations
  in half spaces   We prove that any convex viscosity solution of $\det D^2u=1 $ outside a
bounded domain of $\mathbb{R}^n_+$ tends to a quadratic polynomial at infinity
with rate at least $\frac{x_n}{|x|^{n}}$ if $u$ is a quadratic polynomial on
$\{x_n=0\}$ and satisfies $ \mu|x|^2\leq u\leq \mu^{-1}|x|^2$ as
$|x|\rightarrow \infty$ for some $0<\mu\leq \frac{1}{2}$.

9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg