Existence of solutions for a dynamic Signorini's contact problem

The purpose of this work is to present an existence result for the dynamic frictionless contact problem between an elastic body and a rigid foundation. The proof is based on five fundamental steps: a discretization in time which leads to a discretized problem with unique solution; the construction of functions approximating a solution of the problem; the treatment of the contact condition by means of a Lagrange multiplier whose orthogonality properties allow us to get a priori estimates; the convergence of said functions and, finally, the pass to the limit obtaining a weak solution of the continuous problem.