{
  "abstract": "For a nonnegative, uniformly convex function $Φ$, we study nonnegative minimizers of the quasilinear Alt-Caffarelli energy $\\int_ΩΦ(\\nabla u)+χ_{\\{u>0\\}}$. Under mild regularity assumptions on $Φ$, we show that the codimension of the singular set of the free boundary is at least $2+η$ for a positive $η$. With a singular minimizer in three dimensions in a forthcoming work, this result is sharp as long as integer dimensions are considered. Our proof method is flexible, and we use it to also prove a similar result for minimizers of the $p$-Laplacian counterpart of the Alt-Caffarelli energy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34986",
  "author_total": 3,
  "authors": [
    {
      "name": "Antonio De Rosa"
    },
    {
      "name": "Robin Neumayer"
    },
    {
      "name": "Hui Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mtk1f6r7xmkf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34986",
  "fulltext_url": null,
  "id": "4mtk1f6r7xmkf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34986",
  "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"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223996853",
  "pdf_url": "https://arxiv.org/pdf/2610.34986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mtk1f6r7xmkf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Singular set estimates in quasilinear Alt-Caffarelli problems",
  "title_text": "Singular set estimates in quasilinear Alt-Caffarelli problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/4mtk1f6r7xmkf",
  "venue": "arXiv",
  "versions": []
}