Boundary behavior in the Loewner–Nirenberg problem
Boundary behavior in the Loewner–Nirenberg problem
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DOI：
10.1016/j.jfa.2004.06.014
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发表时间：
2005-05
影响因子：
1.7
通讯作者：
Satyanad Kichenassamy
中科院分区：
文献类型：
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作者：
Satyanad Kichenassamy
设Ω⊂Rn是C2+α，0<；α<；1类的有界域.我们证明了：如果n⩾3和uΩ是方程Δu=n(n-2)u(n+2)/(n-2)在Ω中的最大解，则到边界的双曲半径vΩ=uΩ-2/(n-2)是C2+α类.论证的基础是归结为一个非线性富氏椭圆型偏微分方程组。
Let Ω⊂Rnbe a bounded domain of class C2+α, 0<α<1. We show that if n⩾3 and uΩis the maximal solution of equation Δu=n(n-2)u(n+2)/(n-2)in Ω, then the hyperbolic radius vΩ=uΩ-2/(n-2)is of class C2+αup to the boundary. The argument rests on a reduction to a nonlinear Fuchsian elliptic PDE.