Acta mathematica scientia, Series B >
ELLIPTIC GRADIENT ESTIMATES FOR DIFFUSION OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS
Received date: 2008-06-06
Online published: 2010-09-20
Supported by
The author would like to thank China Scholarship Council for financial support (2007U13020).
In this note, we obtain the elliptic estimate for diffusion operator L = Δ + \nabla\phi\cdot\nabla$ on complete, noncompact Riemannian manifolds, under the curvature condition CD(K, m), which generalizes B. L. Kotschwar's work [5]. As an application, we get estimate on the heat kernel. The Bernstein-type gradient estimate for Schr\"odinger-type gradient is also derived.
Key words： gradient estimate; Bakry-Emery curvature; diffusion operator
JIAN Bin . ELLIPTIC GRADIENT ESTIMATES FOR DIFFUSION OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1555 -1560 . DOI: 10.1016/S0252-9602(10)60148-8
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