  In this work we investigate in detail, the different regimes of the
pioneering work of Chklovskii et al. (1992), which provides an analytical
description to model the electrostatics at the edges of a two-dimensional
electron gas. We take into account full electrostatics and calculate the charge
distribution by solving the 3D Poisson equation self-consistently. The
Chklovskii formalism is reintroduced and is employed to determine the widths of
the incompressible edge-states also considering the spin degree of freedom. It
is shown that, the odd integer filling fractions cannot exist for large
magnetic field intervals if many-body effects are neglected. We explicitly show
that, the incompressible strips which are narrower than the quantum mechanical
length scales vanish. We numerically and analytically show that, the
non-self-consistent picture becomes inadequate considering realistic Hall bar
geometries, predicting large incompressible strips. The details of this picture
is investigated considering device properties together with the many-body and
the disorder effects. Moreover, we provide semi-empirical formulas to estimate
realistic density distributions for different physical boundary conditions.
