WIAS Preprint No. 1962, (2014)

Homogenization and Orowan's law for anisotropic fractional operators of any order



Authors

  • Patrizi, Stefania
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 74Q15 35B27 35R11 82D25

Keywords

  • Crystal dislocation, homogenization, fractional operators

Abstract

We consider an anisotropic fractional operator and we consider the homogenization properties of an evolution equation. The scaling properties and the effective Hamiltonian that we obtain is different according to the fractional parameter. In the isotropic onedimensional case, we also prove a statement related to the so-called Orowan's law, that is an appropriate scaling of the effective Hamiltonian presents a linear behavior.

Appeared in

  • Nonlinear Anal., 119 (2014) pp. 3--36.

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