Homogenization effects on non-local functionals
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914571399200768 |
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| author | Micalizio, Enrico |
| author_facet | Micalizio, Enrico |
| contents | We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the Γ-limit for constant target functions, revealing how the interplay between periodicity and non-locality forces the minimizing sequences to develop highly oscillating microstructures. As a natural consequence, we establish that the effective macroscopic functional fails to admit a standard double-integral representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16627 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homogenization effects on non-local functionals Micalizio, Enrico Analysis of PDEs We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the Γ-limit for constant target functions, revealing how the interplay between periodicity and non-locality forces the minimizing sequences to develop highly oscillating microstructures. As a natural consequence, we establish that the effective macroscopic functional fails to admit a standard double-integral representation. |
| title | Homogenization effects on non-local functionals |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.16627 |