Analysis of a Signorini problem with friction

This paper deals with the study of a nonlinear problem of frictionalcontact between an elastic body and a rigid foundation. Theelastic constitutive law is assumed to be nonlinear and thecontact is modelled with Signorini's conditions and a versionof Coulomb's law of dry friction. We present two weak formulationsof the problem and establish existence and uniqueness results,using arguments of elliptic variational inequalities and a fixed-pintproperty. Moreover, we prove some equivalence results and studythe behaviour of the solution when the coefficient of frictiontends to zero.