We study the existence of solutions to the static contact problem with Coulomb friction in dimension 2, showing different behaviours in isotropic elasticity and in anisotropic elasticity. Our analysis concludes, in 2d, that started in
[Eck C. and Jarušek J., Existence results for the static contact problem with Coulomb friction. Math. Models Methods Appl. Sci. 8(3), 445--468, 1998],
where a technical assumption on the smallness of the friction coefficient was considered. Our technique relies on the proof of the fact that a suitable operator is Leray-Lions, hence in particular pseudo-monotone à la Brézis, and coercive.
This is a joint work with P. Ballard.