The UNIFORM C^(0)ESTIMATE AND WEIGHTED ESTIMATE OF GENERALIZED CHRISTOFFEL-MINKOWSKI PROBLEMS

广义Christo®el-Minkowski问题的一致C^(0)估计和加权估计

In this paper,we consider generalized Christo®el-Minkowski problems as followsσ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),where 0≤l≤k≤n,p-1>0 and f is positive,and we establish the weighted gradient estimate and uniform C^(0)estimate for the positive convex even solutions,which is a generalization of Guan-Xia[1]and Guan[2].

本文考虑了广义Christo®el-Minkowski问题σ_(k)(u_(ij)+uδ_(ij))/σ_(l)(u_(ij)+uδ_(ij))=|u^(p-1)f(x),x∈S^(n),其中0≤l≤k≤n是整数,p-1>0,f是一个正函数.对于上述方程的的正凸偶解,本文建立了解的加权梯度估计和一致C^(0)估计.这是对Guan-Xia[1]和Guan[2]中结果的一般化.