  We investigate a self-gravitating thick domain wall for a $\lambda \Phi^4$
potential. The system of scalar and Einstein equations admits two types of
non-trivial solutions: domain wall solutions and false vacuum-de Sitter
solutions. The existence and stability of these solutions depends on the
strength of the gravitational interaction of the scalar field, which is
characterized by the number $\epsilon$. For $\epsilon \ll 1$, we find a domain
wall solution by expanding the equations of motion around the flat spacetime
kink. For ``large'' $\epsilon$, we show analytically and numerically that only
the de Sitter solution exists, and that there is a phase transition at some
$\epsilon_{\rm max}$ which separates the two kinds of solution. Finally, we
comment on the existence of this phase transition and its relation to the
topology of the domain wall spacetime.
