| 摘要: |
| 本文在Ricci曲率有下界的n维(n≥3)完备黎曼流形上，研究了一类拟线性椭圆方程
\Delta_{p_{1}, \ldots, p_{r}} v=\operatorname{div}\left(\sum_{i=1}^{r}|\nabla v|^{p_{i}-2} \nabla v\right)=0
正解的梯度估计，其中常数满足1
|
| 关键词: 梯度估计 刘维尔型定理 黎曼流形 |
| DOI： |
| 分类号:o175.25 |
| 基金项目: |
|
| Gradient Estimates and Liouville-type Theorems for a Class of Quasilinear Second-order Elliptic Equations |
|
guolan
|
| Abstract: |
| In this paper, we derive gradient estimates of positive solutions to the following quasilinear elliptic equation
\Delta_{p_{1}, \ldots, p_{r}} v=\operatorname{div}\left(\sum_{i=1}^{r}|\nabla v|^{p_{i}-2} \nabla v\right)=0
on n-dimensional (n≥3) complete Riemannian manifolds (M, g) with a lower bound on Ricci curvature, where the constants satisfy1
|
| Key words: Gradient estimates Liouville-type theorems Riemannian manifolds |
