Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4609898 | Journal of Differential Equations | 2016 | 19 Pages |
Abstract
In this paper we establish gradient estimates for positive solutions to the equationequation(0.1)△fup=−λu△fup=−λu on any smooth metric measure space whose m -Bakry–Émery curvature is bounded from below by −(m−1)K−(m−1)K with K≥0K≥0. These estimates imply Liouville theorems for (0.1). When p→1p→1, our main theorem reduces to the gradient estimate of Wang (2010) [9]. As applications, several Harnack inequalities are obtained.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Lin Feng Wang,