  We construct heteroclinic orbits for a strongly nonlocal integro-differential
equation. Since the energy associated to the equation is infinite in such
strongly nonlocal regime, the proof, based on variational methods, relies on a
renormalized energy functional, exploits a perturbation method of viscosity
type and develops a free boundary theory for a double obstacle problem of mixed
local and nonlocal type.
  The description of the stationary positions for the atom dislocation function
in a perturbed crystal, as given by the Peierls-Nabarro model, is a particular
case of the result presented.
