Geodesic
Representation of Harmonic Functions as Potentials and the Cauchy Problem
Matematičeskie zametki, Tome 83 (2008) no. 5, pp. 763-778.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{MZM_2008_83_5_a12,
     author = {Sh. Yarmukhamedov},
     title = {Representation of {Harmonic} {Functions} as {Potentials} and the {Cauchy} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {763--778},
     publisher = {mathdoc},
     volume = {83},
     number = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a12/}
}
TY  - JOUR
AU  - Sh. Yarmukhamedov
TI  - Representation of Harmonic Functions as Potentials and the Cauchy Problem
JO  - Matematičeskie zametki
PY  - 2008
SP  - 763
EP  - 778
VL  - 83
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a12/
LA  - ru
ID  - MZM_2008_83_5_a12
ER  - 
%0 Journal Article
%A Sh. Yarmukhamedov
%T Representation of Harmonic Functions as Potentials and the Cauchy Problem
%J Matematičeskie zametki
%D 2008
%P 763-778
%V 83
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2008_83_5_a12/
%G ru
%F MZM_2008_83_5_a12
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/

[1] M. M. Lavrentev, O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, Izd-vo SO AN SSSR, Novosibirsk, 1962 | MR | Zbl

[2] A. A. Shlyapunov, “O zadache Koshi dlya uravneniya Laplasa”, Sib. matem. zhurn., 33:3 (1992), 205–215 | MR | Zbl

[3] T. Carleman, Les fonctions quasi analitiques, Gauthier-Villars, Paris, 1926

[4] M. M. Lavrentev, “O zadache Koshi dlya uravneniya Laplasa”, Izv. AN SSSR. Ser. matem., 20:6 (1956), 819–842 | MR | Zbl

[5] Sh. Yarmukhamedov, “Funktsiya Karlemana i zadacha Koshi dlya uravneniya Laplasa”, Sib. matem. zhurn., 45:3 (2004), 702–719 | MR | Zbl

[6] M. Ikehata, “Inverse conductivity problem in the infinite slab”, Inverse Problems, 17:3 (2001), 437–454 | DOI | MR | Zbl