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Matematicheskie Zametki, 2008, Volume 83, Issue 5, Pages 763–778
DOI: https://doi.org/10.4213/mzm4721 (Mi mzm4721) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Representation of Harmonic Functions as Potentials and the Cauchy Problem

Sh. Yarmukhamedov

A. Navoi Samarkand State University
Full-text PDF (528 kB) Citations (9)
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DOI: https://doi.org/10.4213/mzm4721
Abstract: 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, Laplace equation, Carleman function, entire function, Green's formula, Lyapunov condition.
Received: 08.08.2005
English version:
Mathematical Notes, 2008, Volume 83, Issue 5, Pages 693–706
DOI: https://doi.org/10.1134/S0001434608050131
Bibliographic databases:
UDC: 515.172.3
Language: Russian
Citation: Sh. Yarmukhamedov, “Representation of Harmonic Functions as Potentials and the Cauchy Problem”, Mat. Zametki, 83:5 (2008), 763–778; Math. Notes, 83:5 (2008), 693–706
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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