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arXiv · 2605.16627

Homogenization effects on non-local functionals

Enrico Micalizio
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Abstract

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 {\Gamma}-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.

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Enrico Micalizio. 2026-05-15. Homogenization effects on non-local functionals. https://doi.org/10.1007/s11587-026-01171-z

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