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

Stefania Patrizi, Enrico Valdinoci

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3-36
Number of pages34
JournalNonlinear Analysis, Theory, Methods and Applications
Volume119
DOIs
Publication statusPublished - 1 Jun 2015
Externally publishedYes

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