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A Probabilistic Approach to Gradient Estimates

Published online by Cambridge University Press:  20 November 2018

M. Cranston
M. Cranston*
Affiliation:
Department of Mathematics Ray P. Hylan Building University of Rochester Rochester, New York 14627 U.S.A.
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Abstract

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Suppose u is a harmonic function on a domain D and x, x' are in D. We estimate |u(x) — u(x')| using two Brownian motions started at x and x' and killed on exiting a cube Q ⊂ D. By selecting appropriate versions of the two Brownian motions, a classical gradient estimate for u is easily derived.

Keywords

60J45.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 46 - 55
Copyright
Copyright © Canadian Mathematical Society 1992

References

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