You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Reflection and Uniqueness Theorems for Harmonic Functions
D. H. Armitage
Proceedings of the American Mathematical Society
Vol. 128, No. 1 (Jan., 2000), pp. 85-92
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/119387
Page Count: 8
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Suppose that h is harmonic on an open half-ball β in RN such that the origin 0 is the centre of the flat part τ of the boundary ∂ β . If h has non-negative lower limit at each point of τ and h tends to 0 sufficiently rapidly on the normal to τ at 0, then h has a harmonic continuation by reflection across τ . Under somewhat stronger hypotheses, the conclusion is that h $\equiv $ 0. These results strengthen recent theorems of Baouendi and Rothschild. While the flat boundary set τ can be replaced by a spherical surface, it cannot in general be replaced by a smooth (N - 1)-dimensional manifold.
Proceedings of the American Mathematical Society © 2000 American Mathematical Society