Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (4): 1185-1194.doi: 10.1007/s10473-019-0420-2

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A NOTE ON LI-YAU-TYPE GRADIENT ESTIMATE

Chengjie YU, Feifei ZHAO   

  1. Department of Mathematics, Shantou University, Shantou 515063, China
  • Received:2018-06-08 Revised:2018-07-13 Online:2019-08-25 Published:2019-09-12
  • Supported by:
    The first author is partially supported by the Yangfan project from Guangdong Province and NSFC (11571215).

Abstract: In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu[21] and Qian[23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.

Key words: Heat equation, Li-Yau-type gradient estimate, heat kernel

CLC Number: 

  • 35K05
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