New Differential Harnack Inequalities for Nonlinear Heat Equations

被引：0
作者：
Jiayong Wu
机构：
[1] Shanghai University,Department of Mathematics
来源：
Chinese Annals of Mathematics, Series B | 2020年 / 41卷
关键词：
Harnack inequality; Nonlinear heat equation; Ricci flow; 53C44;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper deals with constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation ωt = Δω + aω ln ω on closed manifolds. A new interpolated Harnack inequality for ωt = Δω − ω ln ω+εRω on closed surfaces under ε-Ricci flow is also derived. Finally, the author proves a new differential Harnack inequality for ωt = Δω − ω ln ω under Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponential functions, which are superior to time-polynomial functions.
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页码：267 / 284
页数：17
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共 51 条
[1]  
Aronson D(1979)Régularité des solutions de l’équation des milieux poreux dans ℝn, C. R. Acad. Sci. Paris. Sér. A-B 288 A103-A105
[2]  
Bénilan P(2010)Gradient estimates for the heat equation under the Ricci flow J. Funct. Anal. 258 3517-3542
[3]  
Bailesteanua M(2008)Differential Harnack estimates for backward heat equations with potentials under the Ricci flow J. Funct. Anal. 255 1024-1038
[4]  
Cao X-D(2013)Differential Harnack estimates for a nonlinear heat equation J. Funct. Anal. 265 2312-2330
[5]  
Pulemotov A(2015)Harnack estimates for conjugate heat kernel on evolving manifolds Math. Z. 281 201-214
[6]  
Cao X-D(2009)Differential Harnack estimates for time-dependent heat equations with potentials Geom. Funct. Anal. 19 989-1000
[7]  
Cao X-D(2011)Differential Harnack estimates for parabolic equations Proceedings of Complex and Differential Geometry 8 87-98
[8]  
Fayyazuddin Ljungberg B(2011)Pseudolocality for the Ricci flow and applications Canad. J. Math. 63 55-85
[9]  
Liu B-W(1998)Interpolating between Li-Yau’s and Hamilton’s Harnack inequalities on a surface J. Partial Differ. Equ. 11 137-140
[10]  
Cao X-D(1997)Constrained and linear Harnack inqualities for parabolic equations Invent. Math. 129 213-238
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