  The problem of electrostatic screening of a charged line by undoped or weakly
doped graphene is treated beyond the linear-response theory. The induced
electron density is found to be approximately doping independent, n(x)~(log
x)^2/x^2, at intermediate distances x from the charged line. At larger x, twin
p-n junctions may form if the external perturbation is repulsive for graphene
charge carriers. The effect of such inhomogeneities on conductance and quantum
capacitance of graphene is calculated. The results are relevant for transport
properties of graphene grain boundaries and for local electrostatic control of
graphene with ultrathin gates.
