On the exterior Dirichlet problem for Monge–Ampère equations
On the exterior Dirichlet problem for Monge–Ampère equations
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DOI：
10.1016/j.jmaa.2013.04.022
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发表时间：
2013-09
影响因子：
1.3
通讯作者：
Hong-jie Ju;J. Bao
中科院分区：
文献类型：
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作者：
Hong-jie Ju;J. Bao
本文利用Perron方法证明了Rn（n≥2）中一类外区域上的Monge-Ampère方程在无穷远处具有规定渐近行为的粘性解的存在性.这推广了Caffarelli-Li关于det（D2 u）=1的结果。我们还得到了Monge-Ampère方程在无穷远处具有规定渐近行为的整体凸粘性解的存在性。
In this paper, we use the Perron method to prove the existence of viscosity solutions to a class of Monge–Ampère equations on exterior domains in Rn(n≥2) with prescribed asymptotic behavior at infinity. This extends the Caffarelli–Li’s result on det(D2u)=1. We also obtain the existence of entire convex viscosity solutions to the Monge–Ampère equations with prescribed asymptotic behavior at infinity.