PreprintarXiv licencearXiv
Homogenization effects on non-local functionals
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.
Versions
Related
- Quantitative averaging of Markov-modulated additive functionals and Wentzell boundary homogenization
- Emergence of a convex strange term via homogenization of non-local energies at the critical exponent
- A local-to-global principle for f-divergence homogenization
- Partial regularity for local minimizers of functionals with double-phase Orlicz growth
- On Local Inference for Functionals of Ill-Posed Inverse Problems
BibTeX
@misc{micalizio2026homogenization,
title = {{Homogenization effects on non-local functionals}},
author = {Enrico Micalizio},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.16627},
eprint = {2605.16627},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16627},
}
RIS
TY - UNPB
TI - Homogenization effects on non-local functionals
AU - Enrico Micalizio
PY - 2026
DA - 2026/05/15
PB - arXiv
DO - 10.48550/arxiv.2605.16627
UR - https://arxiv.org/abs/2605.16627
AB - 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.
ER -