Weak solvability via bipotentials for contact problems with power-law friction

We study a bilateral contact model with power-law friction and a regularized version of it as well, a regularization of the friction law being considered. The behavior of the material is described by means of a subdifferential inclusion. We deliver a two-field variational formulation via bipotentials for the original problem and also for the regularized version. Subsequently, we study the solvability of the variational formulations we propose, based on abstract auxiliary results. Some properties of the solutions, paying attention to the data dependence, are also investigated. Finally, we deliver a convergence result.