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Eurasian Mathematical Journal, 2014, Volume 5, Number 2, Pages 78–125 (Mi emj158)  

This article is cited in 7 scientific papers (total in 7 papers)

Generalized potentials of double layer in plane theory of elasticity

A. P. Soldatov

Department of mathematical analysis, Belgorod State National Research University
Full-text PDF (586 kB) Citations (7)
References:
Abstract: Connected with the function-theoretic approach, generalized potentials of double layer are introduced for the Lamé system of plane anisotropic elasticity theory. These potentials are constructed for the displacement vector – a solution of the Lamé system, and as well for the conjugate vector–functions describing the stress tensor. There are obtained integral representations of these solutions via potentials mentioned above. As a corollary the first and the second boundary-value problems in different classes (Hölder, Hardy, the class of functions continuous in a closed domain) are reduced to equivalent systems of the boundary Fredholm equations in corresponding spaces.
Keywords and phrases: function-theoretic approach, Lamé system, generalized potentials, plane anisotropic elasticity.
Received: 18.07.2013
Document Type: Article
Language: English
Citation: A. P. Soldatov, “Generalized potentials of double layer in plane theory of elasticity”, Eurasian Math. J., 5:2 (2014), 78–125
Citation in format AMSBIB
\Bibitem{Sol14}
\by A.~P.~Soldatov
\paper Generalized potentials of double layer in plane theory of elasticity
\jour Eurasian Math. J.
\yr 2014
\vol 5
\issue 2
\pages 78--125
\mathnet{http://mi.mathnet.ru/emj158}
Linking options:
  • https://www.mathnet.ru/eng/emj158
  • https://www.mathnet.ru/eng/emj/v5/i2/p78
  • This publication is cited in the following 7 articles:
    1. Koshanov B., Soldatov A., “On Fredholm Solvability and on the Index of the Generalized Neumann Problem For An Elliptic Equation”, Complex Var. Elliptic Equ., 2021  crossref  mathscinet  isi  scopus
    2. Kal'menov T.Sh., Otelbaev M., Arepova G.D., “Bitsadze-Samarskii Boundary Conditions For An Elliptic-Parabolic Volume Potential With Smooth Matching”, Differ. Equ., 56:6 (2020), 740–755  crossref  mathscinet  zmath  isi  scopus
    3. T. Sh. Kal'menov, G. D. Arepova, “Representation of solution of the Dirichlet problem for the Laplace equation in the form of a generalized convolution”, Complex Var. Elliptic Equ., 64:5 (2019), UNSP 040014, 816–824  crossref  mathscinet  zmath  isi  scopus
    4. T. Sh. Kal'menov, G. D. Arepova, “A criterion for the existence of soliton solutions of telegraph equation”, Bull. Karaganda Univ-Math., 91:3 (2018), 45–52  crossref  isi
    5. A. A. Andreyev, V. P. Padchenko, E. A. Kozlova, “To the 70th anniversary of professor alexander pavlovich soldatov”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:1 (2018), 15–22  mathnet  crossref  mathscinet  zmath  isi  elib
    6. A. P. Soldatov, “Mixed problem of plane orthotropic elasticity in a half-plane”, Differ. Equ., 52:6 (2016), 798–812  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Soldatov A.P., “a Plane Elasticity Analogue of the Keldish-Sedov Formula”, 41St International Conference Applications of Mathematics in Engineering and Economics (Amee'15), AIP Conference Proceedings, 1690, eds. Pasheva V., Popivanov N., Venkov G., Amer Inst Physics, 2015, 040004  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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