{
  "abstract": "Alt and Caffarelli proved an Allard-type $ε$-regularity theorem near the flat one-homogeneous minimizer of the one-phase free boundary problem. A natural follow-up question is whether an analogous regularity result holds near singular minimizing cones. In this paper, we prove such an $ε$-regularity theorem near a strongly integrable one-phase minimizing cone with an isolated singularity. More precisely, we show that, after a suitable translation and rotation, the free boundary of any non-degenerate weak solution sufficiently close to the cone is graphical over the free boundary of a leaf of the De Silva--Jerison--Shahgholian foliation. This result is analogous to recent $ε$-regularity theorems in minimal surface theory by Edelen and by Edelen--Spolaor; our proof adapts the strategy of Edelen to the one-phase setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08688",
  "author_total": 1,
  "authors": [
    {
      "name": "Minyoung Jeong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/47dqxc3p3anwt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08688",
  "fulltext_url": null,
  "id": "47dqxc3p3anwt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08688",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08688",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/47dqxc3p3anwt.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08688",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08688"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Regularity of Weak Solutions near Singular Minimizing Cones for the One-Phase Free Boundary Problem",
  "title_text": "Regularity of Weak Solutions near Singular Minimizing Cones for the One-Phase Free Boundary Problem",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/47dqxc3p3anwt",
  "venue": "arXiv",
  "versions": []
}