  In this paper we employ a self-consistent harmonic approximation to
investigate surface melting and local melting close to quantum impurities in
quantum solids. We show that surface melting can occur at temperatures much
lower than the critical temperature $T_c$ of the solid phase instability in the
bulk. Similar effects are driven by the presence of an isotope substitution. In
this latter case, we show that stronger local lattice fluctuations, induced by
a lighter isotope atom, can induce local melting of the host bulk phase.
Experimental consequences and the possible relevance in solid helium are
discussed.
