  In this note we consider the action functional \[ \int_{\mathbb{R} \times
\omega} \left( 1 - \sqrt{ 1 - |\nabla u|^2 } + W(u) \right) \, \mathrm{d}t, \]
where $W$ is a double well potential and $\omega$ is a bounded domain of
$\mathbb{R}^{N-1}$. We prove existence, one-dimensionality and uniqueness (up
to translation) of a smooth minimizing phase transition between the two stable
states $u=1$ and $u=-1$. The question of existence of at least one minimal
heteroclinic connection for the non autonomous model \[ \int_{\mathbb{R}}
\left( 1 - \sqrt{1-|u'|^2} + a(t) W(u) \right) \, \mathrm{d}t \] is also
addressed. For this, we look for the possible assumptions on $a(t)$ ensuring
the existence of a minimizer.
