Geodesic
Representation of Harmonic Functions as Potentials and the Cauchy Problem
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 763-778 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we propose an explicit formula for the reconstruction of a harmonic function in the domain from its known values and from the values of its normal derivative on part of the boundary, i.e., we give an explicit continuation and a regularization formula of the solution of the Cauchy problem for the Laplace equation.
Keywords: harmonic function, potential, Cauchy problem, Carleman function, entire function, Green's formula, Lyapunov condition.
Mots-clés : Laplace equation 
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Sh. Yarmukhamedov. Representation of Harmonic Functions as Potentials and the Cauchy Problem. Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 763-778. http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a12/

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