Homogenization of Lévy-type Operators with Oscillating Coefficients
Moritz Kaßmann, Andrey Lvovich Piatnitski, Е. Г. Жижина · SIAM Journal on Mathematical Analysis · 2019
The paper deals with homogenization of Lévy-type operators with rapidly oscillating coefficients. We consider cases of periodic and random statistically homogeneous micro-structures and show that in the limit we obtain a Lévy-operator. In the periodic case we study both symmetric and non-symmetric kernels whereas in the random case we only investigate symmetric kernels. We also address a nonlinear version of this homogenization problem.