完备黎曼流形上椭圆方程的局部梯度估计

Local Derivative Estimates for an Elliptic Equation on Complete Riemannian Manifolds

本文的主要目的是在一个完备黎曼流形上推导出一个二阶椭圆方程Δfu=plogu+qu的局部梯度估计,该方程具有光滑函数f、p和q。

The main purpose of this paper is to derive local gradient estimates for a second-order elliptic equation ofΔfu=plogu+qu with smooth functions f,p and q on a complete Riemannian man-ifold.