  Following Fr\'enod and Sonnendr\"ucker, we consider the finite Larmor radius
regime for a plasma submitted to a large magnetic field and take into account
both the quasineutrality and the local thermodynamic equilibrium of the
electrons. We then rigorously establish the asymptotic gyrokinetic limit of the
rescaled and modified Vlasov-Poisson system in a three-dimensional setting with
the help of an averaging lemma.

Analysis of PDEs