We present a variational framework for studying screw dislocations subject to
antiplane shear. Using a classical model developed by Cermelli and Gurtin,
methods of Calculus of Variations are exploited to prove existence of
solutions, and to derive a useful expression of the Peach-K\"ohler forces
acting on a system of dislocation. This provides a setting for studying the
dynamics of the dislocations, which is done in a forthcoming work.Comment: 22 page
