Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 31B05, 31B25

Retrieve articles in all journals with MSC (2000): 31B05, 31B25


Additional Information

Richard F. Bass
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: bass@math.uconn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06221-9
PII: S 0002-9939(01)06221-9
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