Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024651 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 17 Pages |
Abstract
In this paper, we study elliptic gradient estimates for a nonlinear f-heat equation, which is related to the gradient Ricci soliton and the weighted log-Sobolev constant of smooth metric measure spaces. Precisely, we obtain Hamilton's and Souplet-Zhang's gradient estimates for positive solutions to the nonlinear f-heat equation only assuming the â-Bakry-Ãmery Ricci tensor is bounded below. As applications, we prove parabolic Liouville properties for some kind of ancient solutions to the nonlinear f-heat equation. Some special cases are also discussed.
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Authors
Jia-Yong Wu,