Calculus of Variations and Geometric Measure Theory

E. Micalizio

Homogenization effects on non-local functionals

created by micalizio on 12 May 2026
modified on 01 Sep 2026

[BibTeX]

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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