  We formulate a variational model for a geometrically necessary screw
dislocation in an anti-plane lattice model at zero temperature. Invariance of
the energy functional under lattice symmetries renders the problem
non-coercive. Nevertheless, by establishing coercivity with respect to the
elastic strain and a concentration compactness principle, we prove existence of
a global energy minimiser and thus demonstrate that dislocations are globally
stable equilibria within our model.
