We consider a model for dislocations in crystals introduced by Koslowski, Cuitiño and Ortiz, whic... more We consider a model for dislocations in crystals introduced by Koslowski, Cuitiño and Ortiz, which includes elastic interactions via a singular kernel behaving as the H 1/2 norm of the slip. We obtain a sharp-interface limit of the model within the framework of Γ-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitté and Seppecher to which their rearrangement argument no longer applies. Instead, we show that the microstructure must be approximately one-dimensional on most length scales and we exploit this property to derive a sharp lower bound.
We consider a model for dislocations in crystals introduced by Koslowski, Cuitiño and Ortiz, whic... more We consider a model for dislocations in crystals introduced by Koslowski, Cuitiño and Ortiz, which includes elastic interactions via a singular kernel behaving as the H 1/2 norm of the slip. We obtain a sharp-interface limit of the model within the framework of Γ-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitté and Seppecher to which their rearrangement argument no longer applies. Instead, we show that the microstructure must be approximately one-dimensional on most length scales and we exploit this property to derive a sharp lower bound.
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Papers by Adriana Bv