  We study bounded, monotone solutions of$\Delta u=W'(u)$ in the whole
of$\R^n$, where$W$ is a double-well potential. We prove that under suitable
assumptions on the limit interface and on the energy growth, $u$ is $1$D.
  In particular, differently from the previous literature, the solution is not
assumed to have minimal properties and the cases studied lie outside the range
of $\Gamma$-convergence methods.
  We think that this approach could be fruitful in concrete situations, where
one can observe the phase separation at a large scale and whishes to deduce the
values of the state parameter in the vicinity of the interface.
  As a simple example of the results obtained with this point of view, we
mention that monotone solutions with energy bounds, whose limit interface does
not contain a vertical line through the origin, are $1$D, at least up to
dimension 4.
