  The density driven Mott transition is studied by means of Dynamical
Mean-Field Theory in the Hubbard-Holstein model, where the Hubbard term leading
to the Mott transition is supplemented by an electron-phonon (e-ph) term. We
show that an intermediate e-ph coupling leads to a first-order transition at
T=0, which is accompanied by phase separation between a metal and an insulator.
The compressibility in the metallic phase is substantially enhanced. At quite
larger values of the coupling a polaronic phase emerges coexisting with a
non-polaronic metal.
