{
  "abstract": "We establish a density property for the obstacle problem of a linearly elastic elliptic membrane shell required to remain confined in a prescribed half-space. For a bounded Lipschitz reference domain, and under the sole assumption that the reference configuration lies at a strictly positive distance from the confining plane, we prove that smooth admissible displacements for which the confinement constraint is inactive (satisfied with a strictly positive margin) are dense in the set of all admissible displacements. This removes the additional condition on the unit normal to the mid-surface required in previous work, and the approximation scheme is elementary and adaptable to other unilateral obstacle problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09570",
  "author_total": 1,
  "authors": [
    {
      "name": "Paolo Piersanti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bs0785vq56dp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09570",
  "fulltext_url": null,
  "id": "2bs0785vq56dp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09570",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "1703|Contact Mechanics and Variational Inequalities"
    ]
  ],
  "openalex": "W7212149797",
  "pdf_url": "https://arxiv.org/pdf/2609.09570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bs0785vq56dp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.09570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09570"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the feasible set of a membrane shell under confinement. Smooth inactive admissible displacements are dense",
  "title_text": "On the feasible set of a membrane shell under confinement. Smooth inactive admissible displacements are dense",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2bs0785vq56dp",
  "venue": "arXiv",
  "versions": []
}