  We study both one and two-phase minimisers of the Dirichlet-area energy
$$E(v) = \int_{B_1} \vert\nabla v\vert^2 + Per(\{v>0\},B_1).$$ In the two-phase
case, we show that the energies $$E_{\varepsilon}(v) = \int_{B_1}\vert\nabla
v\vert^2 + \frac{1}{\varepsilon}W\left(\frac{v}{\varepsilon^{1/2}}\right),$$
$\Gamma$-converge to $E$ as $\varepsilon \to 0$, where $W$ is the double well
potential extended by zero outside of $[-1,1]$ . As a consequence, we show that
bounded local minimisers of $E_{\varepsilon}$ converge to a local minimiser of
$E$.
