Generalized potentials of double layer in plane theory of elasticity

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.