Optimal global asymptotic behavior of the solution to a singular Monge- Ampere equation
Optimal global asymptotic behavior of the solution to a singular Monge- Ampere equation
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奇异 Monge-Ampere 方程解的最优全局渐近行为
DOI：
10.3934/cpaa.2020053
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Zhang Zhijun
中科院分区：
文献类型：
--
作者：
Zhang Zhijun
本文主要研究Monge-Dirichlet方程奇异Dirichlet问题唯一凸解的全局最优渐近性D^2 u=B（x）g（-u），\ u<0，\ x \in \Omega，\ u|_{\partial.\ Omega}=0，$其中$\Omega$是$\mathbb R^n$中的严格凸有界光滑域，其中$n\geq 2$，$g\in C^1（（0，\infty））$是正的，并且在$（0，\infty）$中以$\lim_{s\。rightarrow 0^+}g（s）=\infty$，$B \in C^{\infty}（\Omega）$是positive.in $\Omega$，但可能在边界上消失或爆炸。我们的方法是基于合适的子和超级解决方案的建设。
This paper is mainly concerned with the.optimal global asymptotic behavior of the unique convex solution to a singular.Dirichlet problem for the Monge-Amp\`{e}re equation ${\rm det}.\ D^2 u=b(x)g(-u), \ u<0, \ x \in \Omega, \ u|_{\partial.\Omega}=0,$ where $\Omega$ is a strict convex and bounded smooth.domain in $\mathbb R^n$ with $n\geq 2$, $g\in C^1((0,\infty))$ is positive and decreasing in $(0, \infty)$ with $\lim_{s.\rightarrow 0^+}g(s)=\infty$, $b \in C^{\infty}(\Omega)$ is positive.in $\Omega$, but may vanish or blow up on the boundary properly. Our approach is based on the construction of suitable sub- and super-solutions.