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Local gradient estimates for heat equation on $ RCD^*(k,n)$ metric measure spaces


Author: Jia-Cheng Huang
Journal: Proc. Amer. Math. Soc. 146 (2018), 5391-5407
MSC (2010): Primary 53C23, 35K05
DOI: https://doi.org/10.1090/proc/14185
Published electronically: September 4, 2018
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Abstract: In this paper, we will establish a local gradient estimate and a Liouville type theorem for weak solutions of the heat equation on $ RCD^*(K,N)$ metric measure spaces.


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Additional Information

Jia-Cheng Huang
Affiliation: School of Mathematical Sciences, Fudan University, No. 220, Handan Road, Yangpu District, Shanghai 86200433, People’s Republic of China
Email: hjiach@fudan.edu.cn

DOI: https://doi.org/10.1090/proc/14185
Received by editor(s): December 27, 2017
Received by editor(s) in revised form: April 2, 2018
Published electronically: September 4, 2018
Additional Notes: The author gratefully acknowledges support from the China Postdoctoral Science Foundation, grant number 2017M611438.
Communicated by: Guofang Wei
Article copyright: © Copyright 2018 American Mathematical Society

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