  The effect of neutrino trapping on the longitudinal dielectric function at
low densities has been investigated by using different relativistic mean field
models. Parameter sets G2 of Furnstahl-Serot-Tang and Z271 of
Horowitz-Piekarewicz, along with the adjusted parameter sets of both models,
have been used in this study. The role of the isovector adjustment and the
effect of the Coulomb interaction have been also studied. The effect of the
isovector adjustment is found to be more significant in the
Horowitz-Piekarewicz model, not only in the neutrinoless matter, but also in
the matter with neutrino trapping. Although almost independent to the variation
of the leptonic fraction, the instability region of matter with neutrino
trapping is found to be larger. The presence of more protons and electrons
compared to the neutrinoless case is the reason behind this finding. For
parameter sets with soft equation of states at low density, the appearance of a
large and negative epsilon_L (q, q0 = 0) in some parts of the edge of the
instability region in matter with neutrino trapping is understood as a
consequence of the fact that the Coulomb interaction produced by electrons and
protons interaction is larger than the repulsive isovector interaction created
by the asymmetry between the proton and neutron numbers.
