Orbital free density functional theory of out-of-plane charge screening in graphene

In this talk, we study a Thomas-Fermi-Dirac-von Weizsacker type density functional theory for the response of a single layer of graphene resting on a dielectric substrate to point charges some distance away from the layer. In particular, we obtain results on existence, regularity, and asymptotic decay behavior of the minimizer. This relates to questions in recent physics literature on out-of-plane charge screening in graphene. (Joint with Vitaly Moroz and Cyrill Muratov)