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
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.
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