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.
|Number of pages||34|
|Journal||Nonlinear Analysis, Theory, Methods and Applications|
|Publication status||Published - 1 Jun 2015|