English

$H$-compactness for nonlocal linear operators in fractional divergence form

Analysis of PDEs 2025-10-14 v2

Abstract

We study the HH-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 the HH-convergence of the operators and the Γ\Gamma-convergence of the associated energies.

Keywords

Cite

@article{arxiv.2408.10984,
  title  = {$H$-compactness for nonlocal linear operators in fractional divergence form},
  author = {Maicol Caponi and Alessandro Carbotti and Alberto Maione},
  journal= {arXiv preprint arXiv:2408.10984},
  year   = {2025}
}
R2 v1 2026-06-28T18:18:23.834Z