Weak solutions for antiplane models involving elastic materials with degeneracies

We study the antiplane shear deformation of a cylindrical body in frictional contact with a rigid foundation, under the hypothesis of the small deformations. The envisaged material is assumed to be elastic, physically nonlinear and nonhomogeneous, such that the Lamé coefficient μ satisfies inf_{x ? W} m(x)=0{{rm inf}_{{bf x}inOmega},mu(bf x)=0}, where Ω denotes the cross section of the cylinder. We establish the existence of a unique weak solution for this model on an appropriate weighted functional space. The proof is based on arguments of variational inequalities with strongly monotone operators.