Interpolating between constrained Li-Yau and Chow-Hamilton Harnack inequalities for a nonlinear parabolic equation
arXiv:1109.0128 · doi:10.1016/j.jmaa.2012.06.032
Abstract
We establish a one-parameter family of Harnack inequalities connecting the constrained trace Li-Yau differential Harnack inequality for a nonlinear parabolic equation to the constrained trace Chow-Hamilton Harnack inequality for this nonlinear equation with respect to evolving metrics related to Ricci flow on a 2-dimensional closed manifold. This result can be regarded as a nonlinear version of the previous work of Y. Zheng and the author (Arch. Math. 94 (2010), 591-600).
13 pages; references and explanations added
References in corpus (7)
- Gradient estimates for the heat equation under the Ricci flow
- Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
- Gradient estimates for a nonlinear parabolic equation under Ricci flow
- Gradient estimates for a nonlinear diffusion equation on complete manifolds
- Hamilton type estimates for heat equations on manifolds
- Differential Harnack Estimates for Parabolic Equations
- Gradient estimates for a simple nonlinear heat equation on manifolds