A simple characterization of H-convergence for a class of nonlocal problems

This is a follow-up of the paper J. Fernández-Bonder, A. Ritorto and A. Salort, H-convergence result for nonlocal elliptic-type problems via Tartar’s method, SIAM J. Math. Anal., 49 (2017), pp. 2387–2408, where the classical concept of H-convergence was extended to fractional p-Laplace type operators. In this short paper we provide an explicit characterization of this notion by demonstrating that the weak-∗ convergence of the coefficients is an equivalent condition for H-convergence of the sequence of nonlocal operators. This result takes advantage of nonlocality and is in stark contrast to the local p-Laplacian case.