Dmitry P. Fedchenko, Nikolai Tarkhanov, “Hyperbolic formulas in elliptic Сauchy problems”, J. Sib. Fed. Univ. Math. Phys., 2010, Volume 3, Issue 4,Pages <nobr>419

Hyperbolic formulas in elliptic Сauchy problems

Dmitry P. Fedchenko^a, Nikolai Tarkhanov^b

^a Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
^b Institute of Mathematics, University of Potsdam, Potsdam, Germany

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).

Keywords: Laplace equation, Cauchy problem, wave equation, Carleman formulas.

UDC: 517.955

Received: 10.06.2010
Received in revised form: 10.07.2010
Accepted: 20.08.2010

Language: English