Gradient Estimates and Liouville-Type Theorems for a Nonlinear Elliptic Equation

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Gradient estimate Liouville-Type theorem shrinking gradient Ricci soliton
• 年，卷（期）: 2018,（3）
• 页码范围: 237-251
• 页数: 15页
• 分类号: O175.2
• 语种: 英文
• DOI: 10.4208/jpde.v31.n3.4

摘要

In this paper,we consider the following nonlinear elliptic equation △fu+huα =0on the complete smooth metric space (Rn,g0,e-fdvg0),where g0 is the Euclidean metric on Rn and f =|x|2/4.We prove gradient estimates and Liouville-Type theorems for positive solutions of the above equation.