According to recent experimental and numerical investigations if the
characteristic size of a specimen is in the submicron size regime several new
interesting phenomena emerge during the deformation of the samples. Since in
such a systems the boundaries play a crucial role, to model the plastic
response of submicron sized crystals it is crucial to determine the dislocation
distribution near the boundaries. In this paper a phase field type of continuum
theory of the time evolution of an ensemble of parallel edge dislocations with
identical Burgers vectors, corresponding to the dislocation geometry near
boundaries, is presented. Since the dislocation-dislocation interaction is
scale free (1/r), apart from the average dislocation spacing the theory
cannot contain any length scale parameter. As shown, the continuum theory
suggested is able to recover the dislocation distribution near boundaries
obtained by discrete dislocation dynamics simulations
