We consider an anisotropic Lévy operator Is of any order s∈ (0,1) and we consider the homogenization properties of an evolution equation. The scaling properties and the effective Hamiltonian that we obtain are different according to the cases s<1/2 and s>1/2. In the isotropic one dimensional 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.

Homogenization and Orowan's law for anisotropic fractional operators of any order / S. Patrizi, E. Valdinoci. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 119(2015), pp. 3-36. [10.1016/j.na.2014.07.010]

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

E. Valdinoci
Ultimo
2015

Abstract

We consider an anisotropic Lévy operator Is of any order s∈ (0,1) and we consider the homogenization properties of an evolution equation. The scaling properties and the effective Hamiltonian that we obtain are different according to the cases s<1/2 and s>1/2. In the isotropic one dimensional 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.
Crystal dislocation; Fractional operators; Homogenization; Analysis; Applied Mathematics
Settore MAT/05 - Analisi Matematica
   Elliptic Pdes and Symmetry of Interrfaces and Layers for Odd Nonlinearties
   EPSILON
   EUROPEAN COMMISSION
   FP7
   277749
2015
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/472817
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