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Cauchy's problem for harmonic functions with entire data on a sphere |
Canad. Math. Bull. 40(1997), 60-66
Published:1997-03-01
Printed: Mar 1997
Printed: Mar 1997
- Dmitry Khavinson
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 |