Andaluzia-Cristina Matei
University of Craiova, Craiova, Romania

We consider a class of boundary value problems with physical significance in contact mechanics. More precisely, we draw attention to the weak solvability of a boundary value problem consisting of the Cauchy equilibrium equation, a constitutive law governed by a bipotential, a homogeneous displacement boundary condition, a traction boundary condition, a frictional contact condition modeled with the subdifferential of convex functions and a frictionless contact condition described by means of the Clarke subdifferential. We deliver a weak formulation as a variational-hemivariational system, the unknown being a triple consisting of the displacement field, the Cauchy stress tensor and a Lagrange multiplier related to the friction force on the frictional contact zone. We investigate the existence of the weak solutions by using a fixed point theorem for set-valued mappings and a minimization technique.