数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1349-1364.doi: 10.1016/S0252-9602(12)60104-0

• 论文 • 上一篇    下一篇

LOWER INEQUALITIES OF HEAT SEMIGROUPS BY USING PARABOLIC MAXIMUM PRINCIPLE

胡二彦   

  1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
  • 收稿日期:2010-12-30 修回日期:2011-10-26 出版日期:2012-07-20 发布日期:2012-07-20
  • 基金资助:

    Supported partially by NFSC (11071138).

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).

摘要:

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.

关键词: Dirichlet form, parabolic maximum principle, heat kernel

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

中图分类号: 

  • 47D07