Homogenization of a Class of Integro-Differential Equations with Lévy Operators

Abstract

The periodic homogenization of the integro-differential equation (PIDE) with the Lévy operator with the alpha-stable density, is studied in this paper. The formal asymptotic expansion method is employed to derive the cell problem, the ergodic problem for the Lévy operator without the second-order uniformly elliptic term. The effective equation is then obtained by using the result of the ergodic problem. Finally, the formal argument is justified rigorously by the perturbed test function method.

Keywords:

• Homogenization
• Integro-differential equation
• Lévy operator
• Viscosity solutions

Mathematics Subject Classification:

• 35B27
• 35R12
• 74Q10