  We study energy scaling laws for a simplified, singularly perturbed,
double-well nucleation problem confined in a half-space, in the absence of
gauge invariance and for an inclusion of fixed volume. Motivated by models for
boundary nucleation of a single-phase martensite inside a parental phase of
austenite, our main focus in this nonlocal isoperimetric problem is how the
relationship between the rank-1 direction and the orientation of the half-space
influences the energy scaling with respect to the fixed volume of the
inclusion. Up to prefactors depending on this relative orientation, the scaling
laws coincide with the corresponding ones for bulk nucleation
\cite{knupfer2011minimal} for all rank-1 directions, \textit{but} the ones
normal to the confining hyperplane, where the scaling is as in a three-well
problem in full space, resulting in a lower energy barrier
\cite{Tribuzio-Rueland_1}.
