WEAK SOLUTIONS VIA LAGRANGE MULTIPLIERS FOR CONTACT MODELS WITH NORMAL COMPLIANCE

Abstract

We consider a 3D elastostatic frictional contact problem with normal compliance, which consists of a systems of partial di erential equations associated with a displacement boundary condition, a traction boundary condition and a frictional contact boundary condition. The frictional contact is modeled by means of a normal compliance condition and a version of Coulomb's law of dry friction. After we state the problem and the hypotheses, we deliver a variational formulation as a mixed variational problem with solution-dependent Lagrange multipliers set. Next, we prove the existence and the boundedness of the weak solutions. 1.