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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 $$p$$ 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 $$p$$ p -Laplacian case.

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