Local Aronson–Bénilan estimates for a weighted porous medium equation on Riemannian manifolds

Jiang, Xinrong; Liao, Caisheng

doi:10.1016/j.jmaa.2012.03.018

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Cited by 3 publications

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“…On the other hand, there are analogous entropy formulae for Witten Lapacian on weighted manifold via Bakry‐Émery Ricci curvature , so our results in Theorem can be extended to the case of weighted manifold .…”

Section: Introduction and Main Resultsmentioning

confidence: 73%

Gradient estimates and entropy monotonicity formula for doubly nonlinear diffusion equations on Riemannian manifolds

Wang

Chen

2013

Math Methods in App Sciences

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In the first part of this paper, we prove the sharp global Li‐Yau type gradient estimates for positive solutions to doubly nonlinear diffusion equation(DNDE) on complete Riemannian manifolds with nonnegative Ricci curvature. As an application, one can obtain a parabolic Harnack inequality. In the second part, we obtain a Perelman‐type entropy monotonicity formula for DNDE on compact Riemannian manifolds with nonnegative Ricci curvature. These results generalize some works of Ni (JGA 2004), Lu–Ni–Vázquez–Villani (JMPA 2009) and Kotschwar–Ni (Annales Scientifiques de l'École Normale Supérieure 2009). Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Introduction and Main Resultsmentioning

confidence: 73%