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In this paper, we consider the linearized Vlasov-Poisson equation around anhomogeneous Maxwellian equilibrium in a weakly collisional regime: there is aparameter $\eps$ in front of the collision operator which will tend to $0$.Moreover, we study two cases of collision operators, linear Boltzmann andFokker-Planck. We prove a result of Landau damping for those equations inSobolev spaces uniformly with respect to the collision parameter $\eps$ as itgoes to $0$.

Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime