Gradient estimates and Harnack inequalities for diffusion equation on Riemannian manifolds

被引:0
作者
Yue Wang
机构
[1] China Jiliang University,Department of Mathematics
来源
Frontiers of Mathematics in China | 2010年 / 5卷
关键词
Gradient estimate; Harnack inequality; diffusion equation; Riemannian manifold; 53C21; 58J35;
D O I
暂无
中图分类号
学科分类号
摘要
We derive the gradient estimates and Harnack inequalities for positive solutions of the diffusion equation ut = Δum on Riemannian manifolds. Then, we prove a Liouville type theorem.
引用
收藏
页码:727 / 746
页数:19
相关论文
共 11 条
[1]  
Bonforte M.(2005)Asymptotics of the porous media equation via Sobolev inequalities Journal of Functional Analysis 225 33-62
[2]  
Grillo G.(2006)Global positivity estimates and Harnack inequalities for the fast diffusion equation Journal of Functional Analysis 240 399-428
[3]  
Bonforte M.(1958)An extension of E. Hopf’s maximum principle with an application to Riemannian geometry Duke Math J 25 45-56
[4]  
Vazquez J. L.(1975)Differential equations on Riemannian manifolds and their geometric applications Comm Pure Appl Math 28 333-354
[5]  
Calabi E.(2005)Porous media equation and Sobolev inequalities under negative curvature Bull Sci Math 129 804-830
[6]  
Cheng S. Y.(1991)Gradient estimates and Harnack inequalities for nonlinear parabolic and nonlinear elliptic equations on Riemannian manifolds Journal of Functional Analysis 100 233-256
[7]  
Yau S. T.(1986)On the parabolic kernel of the Schrödinger operator Acta Math 56 153-201
[8]  
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