Localized elliptic gradient estimate for solutions of the heat equation on \({ RCD}^*(K,N)\) metric measure spaces

  • Jia-Cheng Huang
  • Hui-Chun ZhangEmail author


In this paper, we will establish a localized elliptic gradient estimate for weak solutions of the heat equation on metric measure spaces with generalized Ricci curvature bounded from below. One of its main applications is a sharp gradient estimate for the logarithm of heat kernels.

Mathematics Subject Classification



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We thanks the anonymous referees for some suggestions to simplify the argument of Lemma 3.1. Jia-Cheng Huang partially supported by China Postdoctoral Science Foundation funded Project 2017M611438. Hui-Chun Zhang partially supported by NSFC 11521101 and NSFC 11571374.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina
  2. 2.Department of MathematicsSun Yat-sen UniversityGuangzhouChina

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