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Differential Harnack Estimates and Entropy Formulae for Weighted \(\varvec{p}\)-Heat Equations

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In this paper, we obtain various global differential Harnack estimates for positive solutions to weighted p-heat equation on closed smooth metric measure space with a lower m-Bakry-Émery Ricci curvature bound. Moreover, Perelman type \({\mathcal {W}}\)-entropy formulae and Li–Yau type entropy inequalities are derived for weighted p-heat equation on compact with boundary (or no boundary) smooth metric measure space with nonnegative (or negative) m-Bakry-Émery Ricci curvature, which are new in non-weighted case and generalized the results of Kotschwar and Ni (Ann Sci éc Norm Supér 42(1):1–36, 2009) and Wang et al. (Acta Math Sci Ser B Engl Ed 33(4):963–974, 2013).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, Shanxi, China

    Yu-Zhao Wang

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  1. Yu-Zhao Wang
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Correspondence to Yu-Zhao Wang.

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This work is partially supported by the National Science Foundation of China NSFC (11626152).

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Wang, YZ. Differential Harnack Estimates and Entropy Formulae for Weighted \(\varvec{p}\)-Heat Equations. Results Math 71, 1499–1520 (2017). https://doi.org/10.1007/s00025-017-0675-7

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  • DOI: https://doi.org/10.1007/s00025-017-0675-7

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