2020 **Abstract:** This is a follow-up of a paper by , 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.

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“…A more accurate analysis could provide the proof of the weak convergence in X 0 of (26). As far as the authors know, this result has only been proved for certain kind of kernels (see [11,9]). See also [4,Th.…”

confidence: 99%

“…A more accurate analysis could provide the proof of the weak convergence in X 0 of (26). As far as the authors know, this result has only been proved for certain kind of kernels (see [11,9]). See also [4,Th.…”

confidence: 99%

“…Even though there are not so many results about explicit computations of the limit, we can find some theoretical advances. In this sense we must underline [34,11,9].…”

mentioning

confidence: 99%

“…We can find some theoretical advances about the explicit computation of the limit problem. In this sense we must underline among others [35,11,10,50,25]. Much more should be commented about the influence that this type of problems has received from an outstanding list of seminal papers whose main topic, has been the analysis and characterization of Sobolev Spaces.…”

confidence: 99%