Hyperbolic Formulas in Elliptic Cauchy Problems

Details Hyperbolic Formulas in Elliptic Cauchy Problems Hyperbolic Formulas in Elliptic Cauchy Problems

2010-03-18

arxiv.org/abs/1003.3606v1

Physics

Mathematical Physics

16 pages, 4 figures

Scientific paper

We study the Cauchy problem for the Laplace equation in a cylindrical domain
with data on a part of it's boundary which is a cross-section of the cylinder.
On reducing the problem to the Cauchy problem for the wave equation in a
complex domain and using hyperbolic theory we obtain explicit formulas for the
solution, thus developing the classical approach of Hans Lewy (1927).

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