TY - JOUR
T1 - Homogenization and Orowan's law for anisotropic fractional operators of any order
AU - Patrizi, Stefania
AU - Valdinoci, Enrico
PY - 2015/6/1
Y1 - 2015/6/1
N2 - 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.
AB - 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.
KW - Crystal dislocation
KW - Fractional operators
KW - Homogenization
UR - http://www.scopus.com/inward/record.url?scp=84977178426&partnerID=8YFLogxK
U2 - 10.1016/j.na.2014.07.010
DO - 10.1016/j.na.2014.07.010
M3 - Article
AN - SCOPUS:84977178426
VL - 119
SP - 3
EP - 36
JO - Nonlinear Analysis: Theory Methods & Applications
JF - Nonlinear Analysis: Theory Methods & Applications
SN - 0362-546X
ER -