保形曲率方程的爆破解

Blow-up Solutions of Conformal Gaussian Curvature Equations

本文证明了当 K(x)为正 Holder 连续函数时,方程△u-K(X)e^(2(?))=0具无穷边值的古典解在球域上存在;还在较弱的条件下,证明了此类奇边值问题在星形域上具有唯一性.

In this paper,we obtained that there exists the classical solution forthe conformal Gaussian curvature equationsΔu-K(x)e^(2u)=0 with boundarydata+∞ in spherical region B,provided K(x)>0 and K∈c~α(?).Andthe classical solution for the singular boundary value problems in starΩ has the uniqueness provided K(x)>0 and K∈c^0(?).