{
  "abstract": "We look at the inclusion $\\text{d} z_t\\in F(z_t)\\text{d} x_t$, with initial condition $z_0=\\xi$, where $F$ is a nonconvex-valued multifunction, and $x$ a path of bounded $q$-variation, for some $1\\leqslant q<2$, extending the work of Bailleul, Brault, and Coutin (2020). We obtain existence of a global solution to this inclusion without assuming $F$ bounded. We get also a local existence result with a blow-up criterion. If $z(\\xi,x)$ denotes a solution, we obtain measurability of $z$ with respect to $x$ and $\\xi$. To establish this, we introduce a Skorokhod-type distance and prove that Young integration is continuous with respect to it. By the way, we prove that a compact-valued $\\gamma$-Hölder map $F$ has, for any $p>1/\\gamma$ and $\\xi\\in F(0)$, a selection $f(\\xi)$ of bounded $p$-variation, started at $\\xi$, such that $f$ is measurable in $\\xi$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.17112",
  "author_total": 1,
  "authors": [
    {
      "name": "Nathan Benichou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8sf1y1b6r0369.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "8sf1y1b6r0369",
  "issns": [],
  "landing_url": "https://hal.science/hal-05646023v3",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ca"
    ],
    [
      "hal",
      "1.math.math-pr"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05646023/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8sf1y1b6r0369.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:35Z",
      "native_id": "hal-05646023",
      "source": "hal",
      "url": "https://hal.science/hal-05646023v3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ca",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-pr",
      "subfield": "probability"
    }
  ],
  "title": "Unbounded nonconvex Young differential inclusions: existence of a measurable selection of solutions",
  "title_text": "Unbounded nonconvex Young differential inclusions: existence of a measurable selection of solutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:35Z",
  "url": "https://research.draconitic.com/paper/8sf1y1b6r0369",
  "venue": "HAL",
  "versions": []
}