  We establish the $\Gamma$-convergence of some energy functionals describing
nonlocal attractive interactions in bounded domains. The interaction potential
solves an elliptic equation (local or nonlocal) in the bounded domain and the
primary interest of our results is to identify the effects that the boundary
conditions imposed on the potential have on the limiting functional. We
consider general Robin boundary conditions, which include Dirichlet and Neumann
conditions as particular cases. Depending on the order of the elliptic operator
the limiting functional involves the usual perimeter or some fractional
perimeter.
  We also consider the $\Gamma$-convergence of a related energy functional
combining the usual perimeter functional and the nonlocal repulsive interaction
energy.
