Abstract
We present a unified method to derive differential Harnark inequalities for locally positive weak solutions to semilinear parabolic equations on RCD∗(K,N)metric measure spaces, as introduced by Gigli (2015) and Erbar et al. (2015). As its application, on the one hand, we recover many known differential Harnack inequalities on heat equation, on the other hand, for logarithmic type equation and Yamabe type equation, we get some sharp differential Harnack inequalities on RCD∗(0,N)metric measure spaces. As its corollary, we get some sharp Harnack inequalities and Liouville theorems.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
