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Patrizi, Stefania
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Valdinoci, Enrico
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Crystal dislocation
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fractional operators
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homogenization
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2014
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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Author: Patrizi, Stefania
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Start date: 2019
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DDC: 510
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Type: Report
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Version: publishedVersion
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Subject: Crystal dislocation
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WGL Institute: WIAS
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Homogenization and Orowan's law for anisotropic fractional operators of any order
(
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik,
2014
)
Patrizi, Stefania
;
Valdinoci, Enrico
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We consider an anisotropic Lévy operator Is of any order s 2 (0, 1) 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 cases s < 1/2 and s > 1/2. In the isotropic onedimensional case, we also prove a statement related to the so-called Orowans law, that is an appropriate scaling of the effective Hamiltonian presents a linear behavior.
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