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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on the local Hopf's lemma


Author: Vladimir Shklover
Journal: Proc. Amer. Math. Soc. 124 (1996), 2711-2716
MSC (1991): Primary 30B40; Secondary 30C20, 30D50
MathSciNet review: 1327043
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Abstract: The paper deals with the problem of extending the recent work of M.S.Baouendi and L.P.Rothschild concerning harmonic functions vanishing to infinite order in the normal direction in balls and half-spaces. Contrary to what one expects, we show that the B.-R. result extends neither to arbitrary domains nor to cases when the normal is replaced by a curve transversal to the boundary. The exact criterion when the result holds in $\mathbf {R}^2$ is given.


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Additional Information

Vladimir Shklover
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
Address at time of publication: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: shklover@wam.umd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03367-9
PII: S 0002-9939(96)03367-9
Keywords: Harmonic functions, Hopf's lemma, analytic continuation
Received by editor(s): July 6, 1994
Received by editor(s) in revised form: February 28, 1995
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society