Perelman type entropy formulae and differential Harnack estimates for weighted doubly nonlinear diffusion equations under curvature dimension condition
Bull. Korean Math. Soc. 2021 Vol. 58, No. 6, 1539-1561
https://doi.org/10.4134/BKMS.b210087
Published online November 8, 2021
Printed November 30, 2021
Yu-Zhao Wang
Shanxi University
Abstract : We prove Perelman type $\mathcal{W}$-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with $CD(-K,m)$ condition for some $K\ge0$ and $m\ge n$, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities.
Keywords : Weighted doubly nonlinear diffusion equations, Perelman type entropy formula, differential Harnack estimates, Bakry-\'Emery Ricci curvature, curvature dimension condition.
MSC numbers : Primary 58J35, 35K92, 35K55
Supported by : This work was financially supported by NSFC No. 11701347.
Downloads: Full-text PDF   Full-text HTML

   

Copyright © Korean Mathematical Society.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd