Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity

@article{Conti2014ModelingOD,
  title={Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity},
  author={Sergio Conti and Adriana Garroni and Annalisa Massaccesi},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2014},
  volume={54},
  pages={1847-1874}
}
In the modeling of dislocations one is led naturally to energies concentrated on lines, where the integrand depends on the orientation and on the Burgers vector of the dislocation, which belongs to a discrete lattice. The dislocations may be identified with divergence-free matrix-valued measures supported on curves or with 1-currents with multiplicity in a lattice. In this paper we develop the theory of relaxation for these energies and provide one physically motivated example in which the… 

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