Qualitative Stochastic Homogenization of Elliptic Equations With Random Coefficients and Convolutional Potentials
Xiaofeng Jin, Lingwei Ma, Zhenqiu Zhang · Mathematical Methods in the Applied Sciences · 2025
ABSTRACT This paper deals with the homogenization problem for elliptic equations with random statistically homogeneous ergodic coefficients and convolutional potentials in bounded domains. Assuming that the potential has a small absolute expectation, we prove the almost sure qualitative homogenization results in the weak topology in by Tartar's perturbed test function method. Moreover, for bounded ‐domains, with the aid of the sublinear growth properties of correctors, we also prove the qualitative stochastic homogenization results in the strong ‐topology via two‐scale expansion method.