Bull. Korean Math. Soc. 2021; 58(6): 1539-1561
Online first article November 8, 2021 Printed November 30, 2021
https://doi.org/10.4134/BKMS.b210087
Copyright © The Korean Mathematical Society.
Yu-Zhao Wang
Shanxi University
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.
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd