论文标题
关于外部域的Monge-ampère方程的评论
A Remark on Monge-Ampère equation over exterior domains
论文作者
论文摘要
我们改善了Caffarelli-li [Cl03]的结果，对Monge-ampère方程$ u $的无穷大行为$ det（d^2u）= 1 $ on $ \ mathbb {r}^n \ backslash k $ for $ n \ geq 3 $。我们证明，错误项$ o（| x |^{2-n}）$可以改进到$ d（\ sqrt {x'ax}）^{2-n}+o（| x |^{1-n}）$，带有$ d = res [res [res [us] $ us $ u $ $ u $。
We improve the result of Caffarelli-Li [CL03] on the asymptotic behavior at infinity of the exterior solution $u$ to Monge-Ampère equation $det(D^2u)=1$ on $\mathbb{R}^n\backslash K$ for $n\geq 3$. We prove that the error term $O(|x|^{2-n})$ can be refined to $d (\sqrt{x'Ax})^{2-n}+O(|x|^{1-n})$ with $d=Res[u]$ the residue of $u$.
