  We review general domain-wall solutions supported by a delta-function source,
together with a single pure exponential scalar potential in supergravity. These
scalar potentials arise from a sphere reduction in M-theory or string theory.
There are several examples of flat (BPS) domain walls that lead to a
localisation of gravity on the brane, and for these we obtain the form of the
corrections to Newtonian gravity. These solutions are lifted back on certain
internal spheres to D=11 and D=10 as M-branes and D-branes. We find that the
domain walls that can trap gravity yield M-branes or Dp-branes that have a
natural decoupling limit, i.e. p\le 5, with the delta-function source providing
an ultra-violet cut-off in a dual quantum field theory. This suggests that the
localisation of gravity can generally be realised within a Domain-wall/QFT
correspondence, with the delta-function domain-wall source providing a cut-off
from the space-time boundary for these domain-wall solutions. We also discuss
the form of the one-loop corrections to the graviton propagator from the
boundary QFT that would reproduce the corrections to the Newtonian gravity on
the domain wall.
