Singularities of the solutions for the elasticity system in a non homogeneous three-dimensional domain

In this paper we consider the linear Lamé equations in a non homogeneous three-dimensional domain Q composed of two homogeneous bodies Q+ and Q− with the boundary condition: contact without friction-Dirichlet. We first establish the existence and uniqueness results for weak solutions. Then using cylindrical coordinates and assuming that the neighborhood of the edge A is sufficiently small, we give the transcendental equations governing the singular behavior in the spatial case. In the end, applying the results of Merouani (1996), we obtain an explicit description of the singularities for the variational solution of the boundary value problem in the homogeneous case, i.e. the two bodies have the same elasticity coefficients.