Submitted Paper

Inserted: 9 aug 2024
Last Updated: 25 mar 2025

Year: 2024

Abstract:

We study the $H$-convergence of nonlocal linear operators in fractional divergence form, where the oscillations of the matrices are prescribed outside the reference domain. Our compactness argument bypasses the failure of the classical localisation techniques that mismatch with the nonlocal nature of the operators involved. If symmetry is also assumed, we extend the equivalence between $H$-convergence of the operators and $\Gamma$-convergence of the associated energies. As a consequence, we establish the uniqueness of the $H$-limit in the symmetric case.

Keywords: $\Gamma$-convergence, $H$-convergence, Fractional Operators, Riesz potentials

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