On global existence for the Vlasov–Poisson system in a half space

We prove global existence for the Vlasov–Poisson system in a half space in the plasma physics case assuming homogeneous Dirichlet boundary conditions for the electric potential. Our proof uses an adaptation of Pfaffelmoserʹs method and it provides also a different proof of the previously known global existence results for the Vlasov–Poisson system in a half space with Neumann boundary conditions for the electric potential. We also obtain a large class of one-dimensional stationary solutions for the problem with Neumann boundary conditions.