Acta mathematica scientia, Series B >
GRADIENT ESTIMATES AND ENTROPY FORMULAE FOR WEIGHTED p-HEAT EQUATIONS ON SMOOTH METRIC MEASURE SPACES
Received date: 2012-06-11
Revised date: 2012-10-26
Online published: 2013-07-20
Let (M, g, e−fdv) be a smooth metric measure space. In this paper, we con-sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equation
∂u/∂t= efdiv(e−f |∇u|p−2∇u)
on M × [0, ∞), where 1 < p < ∞ and f is a smooth function on M under the assumption that the m-dimensional nonnegative Bakry-Émery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Émery Ricci curva-ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].
WANG Yu-Zhao , YANG Jie , CHEN Wen-Yi . GRADIENT ESTIMATES AND ENTROPY FORMULAE FOR WEIGHTED p-HEAT EQUATIONS ON SMOOTH METRIC MEASURE SPACES[J]. Acta mathematica scientia, Series B, 2013 , 33(4) : 963 -974 . DOI: 10.1016/S0252-9602(13)60055-7
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