Existence theorems in the theory of mixtures

This paper is concerned with boundary-value problems of the linear theory for binary mixtures of elastic bodies. First, a counterpart of the Boussinesq-Somigliana-Galerkin solution in classical elastostatics is established and the fundamental solutions in the equilibrium theory of homogeneous and isotropic mixtures are derived. Then, representations of Somigliana type for the displacement fields are presented. The potentials of single layer and double layer are used to reduce the boundary-value problems to singular integral equations. Existence and uniqueness results are established.