  We prove a theorem for the growth of the energy of bounded, globally
minimizing solutions to a class of semilinear elliptic systems of the form
$\Delta u=\nabla W(u)$, $x\in \mathbb{R}^n$, $n\geq 2$, with $W:\mathbb{R}^m\to
\mathbb{R}$, $m\geq 1$, nonnegative and vanishing at exactly one point (at
least in the closure of the image of the considered solution $u$). As an
application, we can prove a Liouville type theorem under various assumptions.
