Existence of entire solutions of Monge-Ampere equations with prescribed asymptotic behavior
Existence of entire solutions of Monge-Ampere equations with prescribed asymptotic behavior
复制标题
具有规定渐近行为的 Monge-Ampere 方程完整解的存在性
DOI：
10.1007/s00526-019-1639-4
复制
发表时间：
2019
影响因子：
2.1
通讯作者：
Zhou Ziwei
中科院分区：
文献类型：
--
作者：
Bao Jiguang;Xiong Jingang;Zhou Ziwei
证明了在平面无穷远处具有规定渐近行为的monge - ampantere方程全解的存在性，这是2003年Caffarelli-Li未解决的问题。二维问题的特殊困难是由于全局对数项在无穷远处解的渐近展开。在此基础上，给出了由Gálvez-Martínez-Mira于2005年建立的带奇点的monge - amp<e:1>方程解空间的PDE证明。我们也得到了高维情况下一般右边边解的存在性。
We prove the existence of entire solutions of the Monge–Ampère equations with prescribed asymptotic behavior at infinity of the plane, which was left unsolved by Caffarelli–Li in 2003. The special difficulty of the problem in dimension two is due to theglobal logarithmic termin the asymptotic expansion of solutions at infinity. Furthermore, we give a PDE proof of the characterization of the space of solutions of the Monge–Ampère equationwithsingular points, which was established by Gálvez–Martínez–Mira in 2005. We also obtain the existence of solutions in higher dimensional cases with general right hand sides.