  We describe a variational calculation for the problem of screening of a point
charge in a layered correlated metal for dopings close to the Mott transition
where the screening is non-linear due to the proximity to the incompressible
insulating state. We find that external charge can induce locally
incompressible regions and that the non-linear dependence of the screening on
density can induce overscreening in the nearest nearby layers while preserving
overall charge neutrality.
