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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 4, Pages 196–211 (Mi timm1241)  
This article is cited in 2 scientific papers (total in 2 papers)

On the application of the regularization method to the construction of a classical solution of Poisson's equation

È. M. Muhamadieva, G. E. Grishaninab, A. A. Grishaninc

a Vologda State University
b Dubna International University for Nature, Society, and Man
c Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (212 kB) Citations (2)
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Abstract: Necessary and sufficient conditions are found for the existence of a classical solution of Poisson's equation $\Delta u=f$ with continuous function $f$ in a bounded planar domain. By virtue of the known smoothness properties of a generalized harmonic function, these conditions also ensure that all generalized solutions of Poisson's equation are classical in this domain. Particular classes of functions $f$ satisfying the conditions of existence of a classical solution are described.
Keywords: Poisson's equation, classical and generalized solutions, harmonic function, continuous function, strongly continuous function, uniformly strongly continuous function.
Received: 12.01.2015
Bibliographic databases:
Document Type: Article
UDC: 517.951
Language: Russian
Citation: È. M. Muhamadiev, G. E. Grishanina, A. A. Grishanin, “On the application of the regularization method to the construction of a classical solution of Poisson's equation”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 196–211
Citation in format AMSBIB
\Bibitem{MuhGriGri15}
\by \`E.~M.~Muhamadiev, G.~E.~Grishanina, A.~A.~Grishanin
\paper On the application of the regularization method to the construction of a classical solution of Poisson's equation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2015
\vol 21
\issue 4
\pages 196--211
\mathnet{http://mi.mathnet.ru/timm1241}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3468442}
\elib{https://elibrary.ru/item.asp?id=25300997}
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  • https://www.mathnet.ru/eng/timm/v21/i4/p196
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
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