Analysis of a Signorini problem with friction

This paper deals with the study of a nonlinear problem of frictional contac t between an elastic body and a rigid foundation. The elastic constitutive law is assumed to be nonlinear and the contact is modelled with Signorini's conditions and a version of Coulomb's law of dry friction. We present two weak formulations of the problem and establish existence and uniqueness res ults, using arguments of elliptic variational inequalities and a fixed-poin t property. Moreover, we prove some equivalence results and study the behav iour of the solution when the coefficient of friction tends to zero.