Published Paper
Inserted: 12 may 2026
Last Updated: 1 sep 2026
Journal: Ricerche di Matematica
Year: 2026
Doi: 10.1007/s11587-026-01171-z
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 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.
Keywords: Homogenization, $\Gamma$-convergence, Two-scale convergence, Integral representation, non-local functionals, Optimal microstructures
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