Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PERELMAN TYPE ENTROPY FORMULAE AND DIFFERENTIAL HARNACK ESTIMATES FOR WEIGHTED DOUBLY NONLINEAR DIFFUSION EQUATIONS UNDER CURVATURE DIMENSION CONDITION

  • Wang, Yu-Zhao (School of Mathematical Sciences Shanxi University)
  • Received : 2021.01.28
  • Accepted : 2021.07.06
  • Published : 2021.11.30
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Abstract

We prove Perelman type 𝒲-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities.

Keywords

Acknowledgement

This work was financially supported by NSFC No. 11701347.

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