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On harmonic continuation

Published online by Cambridge University Press:  18 May 2009

M. S. P. Eastham
M. S. P. Eastham
Affiliation:
Merton CollegeOxford
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Let D be a bounded, closed, simply-connected domain whose boundary C consists of a finite number of analytic Jordan curves. Let γ be any analytic arc of C. Then we shall prove the following theorem.

Theorem 1. Let u(x, y) be harmonic in the interior of D and continuous on γ, and let ϱu(x, y)/ϱn=g(s) when (x, y) is on γ, where g(s) is an analytic function of arc-length s along γ. Then u(x, y) can be harmonically continued across γ.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 1 , January 1963 , pp. 54 - 56
Copyright
Copyright © Glasgow Mathematical Journal Trust 1963

References

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