  In this paper we study two different ways of coupling a local operator with a
nonlocal one in such a way that the resulting equation is related to an energy
functional. In the first strategy the coupling is given via source terms in the
equation and in the second one a flux condition in the local part appears. For
both models we prove existence and uniqueness of a solution that is obtained
via direct minimization of the related energy functional. In the second part of
this paper we extend these ideas to deal with local/nonlocal elasticity models
in which we couple classical local elasticity with nonlocal peridynamics.
