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A uniqueness theorem for harmonic functions on half-spaces

Published online by Cambridge University Press:  18 May 2009

D. H. Armitage
D. H. Armitage
Affiliation:
Department of Pure Mathematics, The Queen's University of Belfast, Belfast BT7 1NN, Northern Ireland.
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An arbitrary point of the Euclidean space Rn+1, where n > 1, is denoted by (X, y), where X ∈ Rn and y ∈ R, and we denote the Euclidean norm on Rn by ∥·∥. If h is harmonic on the half-space Ω = {(X, y): y > 0}, then we define extended real-valued functions m and M as follows:

and

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 31 , Issue 2 , May 1989 , pp. 189 - 191
Copyright
Copyright © Glasgow Mathematical Journal Trust 1989

References

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