Hyperbolic Formulas in Elliptic Cauchy Problems
Mathematical Physics
2010-03-19 v1 math.MP
Abstract
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).
Cite
@article{arxiv.1003.3606,
title = {Hyperbolic Formulas in Elliptic Cauchy Problems},
author = {D. Fedchenko and N. Tarkhanov},
journal= {arXiv preprint arXiv:1003.3606},
year = {2010}
}
Comments
16 pages, 4 figures