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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  -