Regularity for the Vlasov-Poisson system in a convex domain

We consider the initial-boundary value problem in a convex domain for the Vlasov-Poisson system. Boundary effects play an important role in such physical problems that are modeled by the Vlasov-Poisson system. We establish the global existence of classical solutions with regular initial boundary data under the absorbing boundary condition. We also prove that regular symmetric initial data lead to unique classical solutions for all time in the specular reflection case.