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.
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).
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
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\by M.~Otelbaev, A.~P.~Soldatov
\paper Integral representations of vector functions based on the parametrix of first-order elliptic systems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2021
\vol 61
\issue 6
\pages 967--976
\mathnet{http://mi.mathnet.ru/zvmmf11253}
\crossref{https://doi.org/10.31857/S0044466921030157}
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\transl
\jour Comput. Math. Math. Phys.
\yr 2021
\vol 61
\issue 6
\pages 964--973
\crossref{https://doi.org/10.1134/S0965542521030143}
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Linking options:
https://www.mathnet.ru/eng/zvmmf11253
https://www.mathnet.ru/eng/zvmmf/v61/i6/p967
This publication is cited in the following 6 articles:
A. P. Soldatov, “Integral Representations for Second-Order Elliptic Systems in the Plane”, Comput. Math. and Math. Phys., 64:1 (2024), 118
A. P. Soldatov, “Integralnye predstavleniya dlya ellipticheskikh sistem vtorogo poryadka na ploskosti”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:1 (2024)
Tolib Ishankulov, Mahmud Mannonov, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 3244, INTERNATIONAL SCIENTIFIC CONFERENCE ON MODERN PROBLEMS OF APPLIED SCIENCE AND ENGINEERING: MPASE2024, 2024, 020067
Chan Kuang Vyong, A. P Soldatov, “O fundamental'noy matritse resheniy ploskoy anizotropnoy teorii uprugosti”, Differentsialnye uravneniya, 59:5 (2023), 635
Vuong Tran Quang, A. P. Soldatov, “On the Fundamental Solution Matrix of the Plane Anisotropic Elasticity Theory”, Diff Equat, 59:5 (2023), 646
A. P. Soldatov, “Singular integral operators with a generalized Cauchy kernel”, Dokl. Math., 105:2 (2022), 117–122