  In this paper, we prove a Poincar\'e-type inequality for any set of finite
perimeter which is stable with respect to the free energy among
volume-preserving perturbation, provided that the Hausdorff dimension of its
singular set is at most $n-3$. With this inequality, we classify all the
volume-constraint local energy-minimizing sets in a unit ball, a half-space or
a wedge-shaped domain. In particular, we prove that the relative boundary of
any energy-minimizing set is smooth.
