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

Stefania Patrizi; Enrico Valdinoci

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arXiv · 1610.00203

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

Stefania Patrizi·Enrico Valdinoci

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Abstract

We consider an anisotropic L\'evy operator $\mathcal{I}_s$ of any order $s\in(0,1)$ 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 Orowan's law, that is an appropriate scaling of the effective Hamiltonian presents a linear behavior.

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Stefania Patrizi, Enrico Valdinoci. 2016-10-01. Homogenization and Orowan's law for anisotropic fractional operators of any order. https://arxiv.org/abs/1610.00203

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