A uniqueness result for harmonic functions
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- by Richard F. Bass PDF
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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.References
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Additional Information
- Richard F. Bass
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- Email: bass@math.uconn.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1711-1716
- MSC (2000): Primary 31B05; Secondary 31B25
- DOI: https://doi.org/10.1090/S0002-9939-01-06221-9
- MathSciNet review: 1887018