{
  "abstract": "We study the regularity of the free boundary for a multi-phase obstacle-type problem associated to quadrature domains, which arises from the minimization of the energy $$J(U,F):= \\int_{B_1} (\\frac 1 2 |\\nabla U|^2 + F \\cdot U)dx$$ among all competitors $U=(u^1,\\ldots, u^N)$ with non-negative components $u^i \\geq 0$ with disjoint supports, and constant forcing terms $f^i>0.$ We focus on the geometry of the free boundary at points where at least three distinct components meet (triple junctions).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18270",
  "author_total": 3,
  "authors": [
    {
      "name": "Daniela De Silva"
    },
    {
      "name": "Ovidiu Savin"
    },
    {
      "name": "Henrik Shahgholian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/71e0rgfzfzr5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18270",
  "fulltext_url": null,
  "id": "71e0rgfzfzr5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18270",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221824124",
  "pdf_url": "https://arxiv.org/pdf/2610.18270",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/71e0rgfzfzr5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18270",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18270"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Triple Junctions in Multi-Phase Obstacle type Problems",
  "title_text": "Triple Junctions in Multi-Phase Obstacle type Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/71e0rgfzfzr5d",
  "venue": "arXiv",
  "versions": []
}