Permanent regimes for the Vlasov-Maxwell equations with specular boundary conditions

The subject matter of this paper concerns the existence of permanent regimes (i.e. stationary or time periodic solutions) for the Vlasov-Maxwell system in a bounded domain. We are looking for equilibrium configurations by imposing specular boundary conditions. The main difficulty is the treatment of such boundary conditions. Our analysis relies on perturbative techniques, based on uniform a priori estimates.