Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge

We prove that the Debye screening length emerges in an infinitely extended plasma with uniform background described by the nonlinear Vlasov-Poisson equation, interacting with a point charge. While screened stationary states as well as the time-dependent problem are well-studied for the linearized equation, there are few rigorous results on screening in the nonlinear setting. As such, the results presented here cover the stationary case under the assumptions predicted by the linearized theory.