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Gradient estimates and heat kernel estimates

Published online by Cambridge University Press:  14 November 2011

Zhongmin Qian
Zhongmin Qian
Affiliation:
Applied Mathematics Institute, Shanghai Institute of Railway Technology, 1 Zhennan Road, Shanghai 200333, People's Republic of China
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Extract

In the first part of this paper, Yau's estimates for positive L-harmonic functions and Li and Yau's gradient estimates for the positive solutions of a general parabolic heat equation on a complete Riemannian manifold are obtained by the use of Bakry and Emery's theory. In the second part we establish a heat kernel bound for a second-order differential operator which has a bounded and measurable drift, using Girsanov's formula.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 975 - 990
Copyright
Copyright © Royal Society of Edinburgh 1995

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