Emergence of a convex strange term via homogenization of non-local energies at the critical exponent
Abstract
We derive the Γ-limit of convolution-type and discrete energies subject to Dirichlet boundary conditions on periodically perforated domains at the critical exponent. We assume that the length-scale of the non-local interactions is much smaller than the side-length of the cubic perforations and prove that a separation of scales occurs. Exploiting the analogies between the variational frameworks of our interest, we employ a unified argument to overcome the technical difficulties that arise from the scaling invariance of the energies. Our multiscale analysis yields a novel observation that is not related to the non-local nature of the functionals, but rather to the analysis at the critical exponent: we prove that the energy density of the strange term is convex, even in the vector-valued setting.
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BibTeX
@misc{brusca2026emergence,
title = {{Emergence of a convex strange term via homogenization of non-local energies at the critical exponent}},
author = {Giuseppe Cosma Brusca and Giuliana Fusco},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11371},
eprint = {2609.11371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11371},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emergence of a convex strange term via homogenization of non-local energies at the critical exponent
AU - Giuseppe Cosma Brusca
AU - Giuliana Fusco
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11371
UR - https://arxiv.org/abs/2609.11371
AB - We derive the Γ-limit of convolution-type and discrete energies subject to Dirichlet boundary conditions on periodically perforated domains at the critical exponent. We assume that the length-scale of the non-local interactions is much smaller than the side-length of the cubic perforations and prove that a separation of scales occurs. Exploiting the analogies between the variational frameworks of our interest, we employ a unified argument to overcome the technical difficulties that arise from the scaling invariance of the energies. Our multiscale analysis yields a novel observation that is not related to the non-local nature of the functionals, but rather to the analysis at the critical exponent: we prove that the energy density of the strange term is convex, even in the vector-valued setting.
ER -