PreprintCC BY 4.0arXiv
The Bourgain, Brezis, Mironescu localization for deterministic obstacle problems
Abstract
We study the asymptotic behaviour of families of fractional energies normalized according to the Bourgain--Brezis--Mironescu formula and defined on functions satisfying a pinning condition on possibly aperiodic families of small obstacles. The result of the simultaneous limit depends crucially on the critical rescaling chosen for the obstacles.
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BibTeX
@misc{focardi2026bourgain,
title = {{The Bourgain, Brezis, Mironescu localization for deterministic obstacle problems}},
author = {Matteo Focardi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25515},
eprint = {2610.25515},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25515},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Bourgain, Brezis, Mironescu localization for deterministic obstacle problems
AU - Matteo Focardi
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25515
UR - https://arxiv.org/abs/2610.25515
AB - We study the asymptotic behaviour of families of fractional energies normalized according to the Bourgain--Brezis--Mironescu formula and defined on functions satisfying a pinning condition on possibly aperiodic families of small obstacles. The result of the simultaneous limit depends crucially on the critical rescaling chosen for the obstacles.
ER -