Geodesic
Hyperbolic formulas in elliptic Сauchy problems
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 4, pp. 419-432

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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: Cauchy problem, wave equation
Mots-clés : Laplace equation, Carleman formulas. 
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Dmitry P. Fedchenko; Nikolai Tarkhanov. Hyperbolic formulas in elliptic Сauchy problems. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 4, pp. 419-432. http://geodesic.mathdoc.fr/item/JSFU_2010_3_4_a0/