Acta mathematica scientia, Series B >
LOWER INEQUALITIES OF HEAT SEMIGROUPS BY USING PARABOLIC MAXIMUM PRINCIPLE
Received date: 2010-12-30
Revised date: 2011-10-26
Online published: 2012-07-20
Supported by
Supported partially by NFSC (11071138).
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
HU Er-Yan . LOWER INEQUALITIES OF HEAT SEMIGROUPS BY USING PARABOLIC MAXIMUM PRINCIPLE[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1349 -1364 . DOI: 10.1016/S0252-9602(12)60104-0
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