A Uniqueness Criterion for the Signorini Problem with Coulomb Friction

The purpose of this paper is to study the solutions to the Signorini problem with Coulomb friction (the so-called Coulomb problem). Some optimal a priori estimates are given and a uniqueness criterion is exhibited. Recently, nonuniqueness examples have been presented in the continuous framework. It is proven, here, that if a solutions satisfies a certain hypothesis on the tangential displacement and if the friction coefficient is small enough, it is the unique solution to the problem. In particular, this result can be useful for the search of multi-solutions to the Coulomb problem, because it eliminates a lot of uniqueness situations.