  We study nonlocal integral equations on bounded domains with finite-range
nonlocal interactions that are localized at the boundary. We establish a
Green's identity for the nonlocal operator that recovers the classical boundary
integral, which, along with the variational analysis established previously,
leads to the well-posedness of these nonlocal problems with various types of
classical local boundary conditions. We continue our analysis via
boundary-localized convolutions, using them to analyze the Euler-Lagrange
equations, which permits us to establish global regularity properties and
classical Sobolev convergence to their classical local counterparts.
