  The second-order singularly-perturbed problem concerns the integral
functional $\int_\Omega \varepsilon_n^{-1}W(u) +
\varepsilon_n^3\|\nabla^2u\|^2\,dx$ for a bounded open set $\Omega \subseteq
\mathbb{R}^N$, a sequence $\varepsilon_n \to 0^+$ of positive reals, and a
function $W:\mathbb{R} \to [0,\infty)$ with exactly two distinct zeroes. This
functional is of interest since it models the behavior of phase transitions,
and its Gamma limit as $n \to \infty$ was studied by Fonseca and Mantegazza. In
this paper, we study an instance of the problem for $N=1$. We find a different
form for the Gamma limit, and study the Gamma limit under the addition of
boundary data.
