  We consider a one-dimensional McKean-Vlasov SDE on a domain and the
associated mean-field interacting particle system. The peculiarity of this
system is the combination of the interaction, which keeps the average position
prescribed, and the reflection at the boundaries; these two factors make the
effect of reflection non local. We show pathwise well-posedness for the
McKean-Vlasov SDE and convergence for the particle system in the limit of large
particle number.
