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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.18697 |
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| _version_ | 1866918257726849024 |
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| author | Brusca, Giuseppe Cosma |
| author_facet | Brusca, Giuseppe Cosma |
| contents | 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 $λ\in(0,+\infty)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiscale homogenization of non-local energies of convolution-type Brusca, Giuseppe Cosma Analysis of PDEs Optimization and Control 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 $λ\in(0,+\infty)$. |
| title | Multiscale homogenization of non-local energies of convolution-type |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2512.18697 |