{
  "abstract": "In this paper, we continue our recent study on anisotropic minimal surface equation with free boundary condition in Wang-Wei-Xia-Zhang (Arch Ration Mech Anal 250:42, 2026). The first main result solves the corresponding mixed boundary value problem. As an application, we prove the following Bernstein-type theorem: any anisotropic minimal graph over $\\mathbb{R}^3_+$ with free boundary must be flat. These extend the classical results of Simon (Indiana Univ Math J 25:821--855, 1976; Math Z 154:265--273, 1977) to an appropriate free boundary setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12630",
  "author_total": 4,
  "authors": [
    {
      "name": "Guofang Wang"
    },
    {
      "name": "Wei Wei"
    },
    {
      "name": "Chao Xia"
    },
    {
      "name": "Xuwen Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5s0yw2e20mfn0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12630",
  "fulltext_url": null,
  "id": "5s0yw2e20mfn0",
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  "landing_url": "https://arxiv.org/abs/2609.12630",
  "language": null,
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  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7213133275",
  "pdf_url": "https://arxiv.org/pdf/2609.12630",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5s0yw2e20mfn0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12630",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12630"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Bernstein theorem for $3$-dimensional anisotropic minimal graphs with free boundary",
  "title_text": "Bernstein theorem for $3$-dimensional anisotropic minimal graphs with free boundary",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/5s0yw2e20mfn0",
  "venue": "arXiv",
  "versions": []
}