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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 harmonic functions, Cauchy's problem, homogeneous harmonics
MSC Classifications: 35B60, 31B20 show english descriptions Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]
Boundary value and inverse problems
35B60 - Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]
31B20 - Boundary value and inverse problems
 

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