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# Cauchy's problem for harmonic functions with entire data on a sphere

Published:1997-03-01
Printed: Mar 1997
• Dmitry Khavinson
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## Abstract

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 ${\bf R}^N$ except, perhaps, for the center of the sphere.
 Keywords: harmonic functions, Cauchy's problem, homogeneous harmonics
 MSC Classifications: 35B60 - Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] 31B20 - Boundary value and inverse problems

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