  Within the framework of Hilbert spaces, we solve nonlocal problems in bounded
domains with prescribed conditions on the complement of the domain. Our main
focus is on the inhomogeneous Neumann problem in a rather general setting. We
also study the transition from complement value problems to local boundary
value problems. Several results are new even for the fractional Laplace
operator. The setting also covers relevant models in the framework of
peridynamics.
