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A uniqueness result for harmonic functions

Author: Richard F. Bass
Journal: Proc. Amer. Math. Soc. 130 (2002), 1711-1716
MSC (2000): Primary 31B05; Secondary 31B25
Published electronically: October 24, 2001
MathSciNet review: 1887018
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Abstract: Let $d\geq 2$, $D=\mathbb{R}^{d}\times (0,\infty )$, and suppose $u$ is harmonic in $D$ and $C^{2}$ on the closure of $D$. If the gradient of $u$vanishes continuously on a subset of $\partial D$ of positive $d$-dimensional Lebesgue measure and $u$ satisfies certain regularity conditions, then $u$ must be identically constant.

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Additional Information

Richard F. Bass
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269

Keywords: Harmonic, Privalov, unique continuation, diffusions, Bessel processes
Received by editor(s): July 16, 2000
Received by editor(s) in revised form: December 5, 2000
Published electronically: October 24, 2001
Additional Notes: This research was partially supported by NSF Grant DMS 9700721.
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2001 American Mathematical Society

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