{
  "abstract": "In this paper, we study the regularity of free boundaries for Monge-Ampère obstacle problem up to the boundary. We mainly focus on how the growth order of boundary value near the contact point impact the regularity. We also find an interesting phenomena that under quadratic growth boundary value, the free boundary enjoys better regularity in high dimensions than in two dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08351",
  "author_total": 2,
  "authors": [
    {
      "name": "Hanfei Han"
    },
    {
      "name": "Genggeng Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5mewcd7xrs7mc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08351",
  "fulltext_url": null,
  "id": "5mewcd7xrs7mc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08351",
  "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": "W7220937083",
  "pdf_url": "https://arxiv.org/pdf/2610.08351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5mewcd7xrs7mc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Regularity of Free Boundary for Monge-Ampère Obstacle Problem up to the Boundary",
  "title_text": "Regularity of Free Boundary for Monge-Ampère Obstacle Problem up to the Boundary",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/5mewcd7xrs7mc",
  "venue": "arXiv",
  "versions": []
}