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Search: MSC category 35B60 ( Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx] )

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1. CMB 1997 (vol 40 pp. 60)

Khavinson, Dmitry
 Cauchy's problem for harmonic functions with entire data on a sphere 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 harmonicsCategories:35B60, 31B20
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