Submitted Paper

Inserted: 9 aug 2024
Last Updated: 21 aug 2024

Year: 2024

Abstract:

We study the $H$-convergence problem for a class 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 show that the $H$-compactness can be equivalently obtained through the $\Gamma$-convergence of the associated energies.

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

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