{"ID":2826534,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.18697","arxiv_id":"2512.18697","title":"Multiscale homogenization of non-local energies of convolution-type","abstract":"We analyze a family of non-local integral functionals of convolution-type depending on two small positive parameters $\\varepsilon,δ$: the first rules the length-scale of the non-local interactions and produces a `localization' effect as it tends to $0$, the second is the scale of oscillation of a finely inhomogeneous periodic structure in the domain. We prove that a separation of the two scales occurs and that the interplay between the localization and homogenization effects in the asymptotic analysis is determined by the parameter $λ$ defined as the limit of the ratio $\\varepsilon/δ$. We compute the $Γ$-limit of the functionals with respect to the strong $L^p$-topology for each possible value of $λ$ and detect three different regimes, the critical scale being obtained when $λ\\in(0,+\\infty)$.","short_abstract":"We analyze a family of non-local integral functionals of convolution-type depending on two small positive parameters $\\varepsilon,δ$: the first rules the length-scale of the non-local interactions and produces a `localization' effect as it tends to $0$, the second is the scale of oscillation of a finely inhomogeneous p...","url_abs":"https://arxiv.org/abs/2512.18697","url_pdf":"https://arxiv.org/pdf/2512.18697v1","authors":"[\"Giuseppe Cosma Brusca\"]","published":"2025-12-21T11:23:19Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}