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Cauchy’s Problem for Harmonic Functions with Entire Data on a Sphere

Published online by Cambridge University Press:  20 November 2018

Dmitry Khavinson
Dmitry Khavinson*
Affiliation:
Department of Mathematics University of Arkansas Fayetteville, Arkansas 72701 U.S.A., email: dmitry@comp.uark.edu
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Abstract

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We give an elementary potential-theoretic proof of a theorem of G. Johnsson: all solutions of Cauchy’s problems for the Laplace equations with an entire data on a sphere extend harmonically to the whole space RN except, perhaps, for the center of the sphere.

Keywords

35B6031B20harmonic functionsCauchy’s problemhomogeneous harmonics
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 1 , 01 March 1997 , pp. 60 - 66
Copyright
Copyright © Canadian Mathematical Society 1997

References

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