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Journal of Siberian Federal University. Mathematics & Physics, 2010, Volume 3, Issue 4, Pages 419–432 (Mi jsfu142)  
Hyperbolic formulas in elliptic Сauchy problems

Dmitry P. Fedchenkoa, Nikolai Tarkhanovb

a Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia
b Institute of Mathematics, University of Potsdam, Potsdam, Germany
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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.
Received: 10.06.2010
Received in revised form: 10.07.2010
Accepted: 20.08.2010
Document Type: Article
UDC: 517.955
Language: English
Citation: Dmitry P. Fedchenko, Nikolai Tarkhanov, “Hyperbolic formulas in elliptic Сauchy problems”, J. Sib. Fed. Univ. Math. Phys., 3:4 (2010), 419–432
Citation in format AMSBIB
\Bibitem{FedTar10}
\by Dmitry~P.~Fedchenko, Nikolai~Tarkhanov
\paper Hyperbolic formulas in elliptic Сauchy problems
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2010
\vol 3
\issue 4
\pages 419--432
\mathnet{http://mi.mathnet.ru/jsfu142}
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