  We outline a Kohn-Sham-Dirac density-functional-theory (DFT) scheme for
graphene sheets that treats slowly-varying inhomogeneous external potentials
and electron-electron interactions on an equal footing. The theory is able to
account for the the unusual property that the exchange-correlation contribution
to chemical potential increases with carrier density in graphene. Consequences
of this property, and advantages and disadvantages of using the DFT approach to
describe it, are discussed. The approach is illustrated by solving the
Kohn-Sham-Dirac equations self-consistently for a model random potential
describing charged point-like impurities located close to the graphene plane.
The influence of electron-electron interactions on these non-linear screening
calculations is discussed at length, in the light of recent experiments
reporting evidence for the presence of electron-hole puddles in nearly-neutral
graphene sheets.
