{
  "abstract": "We consider a family of non-local and non-convex functionals depending on three real parameters $(γ,p,λ)$, which was introduced by H. Brezis, A. Seeger, J. Van Schaftingen and P. L. Yung. In the case $γ<-p$ we prove a lower bound for the Gamma-liminf of these functionals as $λ\\to 0^+$ and a Poincaré-type inequality. We also show that such inequality cannot hold if $γ>0$, and we establish a modified version in this case. These results answer some open questions posed by these authors and by H. M. Nguyen.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05929",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicola Picenni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpe6cn6mxrn2y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05929",
  "fulltext_url": null,
  "id": "cpe6cn6mxrn2y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05929",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220706678",
  "pdf_url": "https://arxiv.org/pdf/2610.05929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpe6cn6mxrn2y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05929"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lower bounds and Poincaré inequality for the Brezis-Seeger-Van Schaftingen-Yung functionals",
  "title_text": "Lower bounds and Poincaré inequality for the Brezis-Seeger-Van Schaftingen-Yung functionals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/cpe6cn6mxrn2y",
  "venue": "arXiv",
  "versions": []
}