Abstract
We obtain a formula which expresses the values of a harmonic function at points of a threedimensional domain in terms of its values and the values of its normal derivative on a portion of the domain boundary.
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A. N. Tikhonov, “On the stability of inverse problems,” Dokl. Akad. Nauk SSSR,39, No. 5, 195–198 (1943).
M. M. Lavrent'ev, Some Ill-Posed Problems of Mathematical Physics [in Russian], Izd. Sibirsk. Otdel. Akad. Nauk SSSR (1962).
A. N. Tikhonov, “On the solution of ill-posed problems and a method of regularization,” Dokl. Akad. Nauk SSSR,151, No. 3, 501–504 (1963).
V. K. Ivanov, “On ill-posed problems,” Matem. Sb.,61, No. 2, 211–223 (1963).
T. Carleman, Les Fonctions Quasi Analytiques, Gauthier-Villars, Paris (1926).
S. N. Mergelyan, “Studies in the theory of functions of a complex variable,” Usp. Matem. Nauk,11, No. 5, 3–26 (1956).
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Translated from Matematicheskie Zametki, Vol. 18, No. 1, pp. 57–61, July, 1975.
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Yarmukhamedov, S. On a Cauchy problem for Laplace's equation. Mathematical Notes of the Academy of Sciences of the USSR 18, 615–618 (1975). https://doi.org/10.1007/BF01461141
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DOI: https://doi.org/10.1007/BF01461141