Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (4): 1349-1364.doi: 10.1016/S0252-9602(12)60104-0

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LOWER INEQUALITIES OF HEAT SEMIGROUPS BY USING PARABOLIC MAXIMUM PRINCIPLE

 HU Er-Yan   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • Received:2010-12-30 Revised:2011-10-26 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    Supported partially by NFSC (11071138).

Abstract:

Using parabolic maximum principle, we apply the analytic method to obtain lower comparison inequalities for non-negative weak supersolutions of the heat equation associated with a regular strongly ρ-local Dirichlet form on the abstract metric measure space. As an application, we obtain lower estimates for heat kernels on some Riemannian manifolds.

Key words: Dirichlet form, parabolic maximum principle, heat kernel

CLC Number: 

  • 47D07
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