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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 6, Pages 967–976
DOI: https://doi.org/10.31857/S0044466921030157 (Mi zvmmf11253) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Partial Differential Equations

Integral representations of vector functions based on the parametrix of first-order elliptic systems

M. Otelbaeva, A. P. Soldatovbc

a International Information Technology University
b Federal Research Center "Informatics and Management", Russian Academy of Sciences, 119333, Moscow, Russia
c Moscow Center for Fundamental and Applied Mathematics, 119991, Moscow, Russia
Citations (4)
DOI: https://doi.org/10.31857/S0044466921030157
Abstract: Generalized integrals are introduced with kernels depending on the difference of the arguments taken over a domain and a smooth contour, the boundary of this domain. These kernels arise as parametrixes of first-order elliptic systems with variable coefficients. Using such integrals (with complex density over the domain and real density over the contour), representations of vector functions that are smooth in the closed domain are described. The Fredholmity of the representation obtained in the corresponding Banach spaces is established.
Key words: Pompeiu and Cauchy integrals, bounded operator, Fredholmity, parametrix, elliptic systems.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AR 08857604
The work of M. Otelbaev was supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AR 08857604).
Received: 06.08.2020
Revised: 06.08.2020
Accepted: 18.11.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 6, Pages 964–973
DOI: https://doi.org/10.1134/S0965542521030143
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: M. Otelbaev, A. P. Soldatov, “Integral representations of vector functions based on the parametrix of first-order elliptic systems”, Zh. Vychisl. Mat. Mat. Fiz., 61:6 (2021), 967–976; Comput. Math. Math. Phys., 61:6 (2021), 964–973
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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