Calculus of Variations and Geometric Measure Theory

E. Micalizio

Homogenization effects on non-local functionals

created by micalizio on 12 May 2026

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Preprint

Inserted: 12 may 2026
Last Updated: 12 may 2026

Year: 2026

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.


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