GRADIENT AND HARNACK INEQUALITIES ON NONCOMPACT MANIFOLDS WITH BOUNDARY

被引:11
作者
Wang, Feng-Yu [1 ,2 ]
机构
[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China
[2] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales
基金
中国国家自然科学基金;
关键词
gradient estimate; Harnack inequality; generalized maxium principle; NEUMANN EIGENVALUE; OPERATOR; KERNEL;
D O I
10.2140/pjm.2010.245.185
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
By using the reflecting diffusion process and a conformal change of metric, a generalized maximum principle is established for (unbounded) time-space functions on a class of noncompact Riemannian manifolds with (nonconvex) boundary. As applications, Li-Yau-type gradient and Harnack inequalities are derived for the Neumann semigroup on a class of noncompact manifolds with (nonconvex) boundary. These generalize some previous ones obtained for the Neumann semigroup on compact manifolds with boundary. As a byproduct, the gradient inequality for the Neumann semigroup derived by Hsu on a compact manifold with boundary is confirmed on these noncompact manifolds.
引用
收藏
页码:185 / 200
页数:16
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