WIAS Preprint No. 1894, (2013)

Strongly nonlocal dislocation dynamics in crystals


  • Dipierro, Serena
  • Figalli, Alessio
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 49N60 35B05 35Q99 35B40 35J25 35D30 35G25


  • nonlocal Peierls-Nabarro model, dislocation dynamics, fractional Laplacian, oscillation and regularity results




We consider an equation motivated by crystal dynamics and driven by a strongly nonlocal elliptic operator of fractional type. We study the evolution of the dislocation function for macroscopic space and time scales, by showing that the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. We also prove that the motion of these dislocation points is governed by an interior repulsive potential that is superposed to an elastic reaction to the external stress.

Appeared in

  • Comm. Partial Differential Equations, 39 (2014) pp. 2351--2387.

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