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

Renormalized Energy and Peach-K\"ohler Forces for Screw Dislocations with Antiplane Shear