Geodesic
Generalized potentials of double layer in plane theory of elasticity
Eurasian mathematical journal, Tome 5 (2014) no. 2, pp. 78-125

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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. 
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     author = {A. P. Soldatov},
     title = {Generalized potentials of double layer in plane theory of elasticity},
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A. P. Soldatov. Generalized potentials of double layer in plane theory of elasticity. Eurasian mathematical journal, Tome 5 (2014) no. 2, pp. 78-125. http://geodesic.mathdoc.fr/item/EMJ_2014_5_2_a4/