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A gradient estimate on a manifold with convex boundary

Published online by Cambridge University Press:  14 November 2011

Zhongmin Qian
Zhongmin Qian
Affiliation:
Department of Mathematics, Imperial College of Science, Technology and Medicine, 180 Queen's Gate, London SW7 2BZ, U.K
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Abstract

We present a simple probability approach for establishing a gradient estimate for a solution of an elliptic equation on a compact Riemannian manifold with convex boundary, or on a noncompact complete manifold. Our method can also be applied to derive a similar gradient estimate for a nonlinear parabolic equation, and an abstract gradient estimate for a Markov semigroup.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 1 , 1997 , pp. 171 - 179
Copyright
Copyright © Royal Society of Edinburgh 1997

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