A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
作者: Abimbola Abolarinwa
作者单位: 1UNIVERSITY OF SUSSEX, BRIGHTON, BN1 9QH, UK.
刊名: International Journal of Analysis and Applications, 2014, Vol.6 (1)
来源数据库: Etamaths Journal
原始语种摘要: In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.
全文获取路径: Etamaths Publishing  (合作)
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关键词翻译
关键词翻译
  • entropy 平均信息量
  • generalized 广义
  • kernel 
  • manifold 多样性
  • gradient 倾斜度
  • metric 米制的
  • formulas 公式
  • pointwise 逐点
  • equation 方程
  • estimates 估值