Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1896236 | Journal of Geometry and Physics | 2012 | 6 Pages |
Abstract
In this short note, we obtain a “ΦΦ-gradient estimate” for bounded solutions to the heat equation on compact Riemannian manifolds, which generalizes the well-known Hamilton gradient estimate [R.S. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1 (1993) 113–126]. We derive as applications some useful estimates for the ΦΦ-entropy and the associated heat kernel.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Bin Qian,