  Starting from a microscopic description of a system of strongly interacting
electrons in a strong magnetic field in a finite geometry, we construct the
boundary low energy effective theory for a fractional quantum Hall droplet
taking into account the effects of a smooth edge. The effective theory obtained
is the standard chiral boson theory (chiral Luttinger theory) with an
additional self-interacting term which is induced by the boundary. As an
example of the consequences of this model, we show that such modification leads
to a non-universal reduction in the tunnelling exponent which is independent of
the filling fraction. This is in qualitative agreement with experiments, that
systematically found exponents smaller than those predicted by the ordinary
chiral Luttinger liquid theory.
