{
  "abstract": "We study the far-field behavior of solutions of the one-phase Bernoulli free boundary problem in the exterior of a ball, and of entire solutions with a single compactly supported inhomogeneity of the free boundary condition, which we call a defect. For solutions which blow down to a half-plane solution (proper solutions) we establish an asymptotic expansion at infinity: in dimension $d \\geq 3$ the free boundary height converges to a limit at rate $|x|^{2-d}$ with a capacity-type coefficient, while in dimension $d=2$ the expansion carries a logarithmic term. A significant novelty is that the expansions are quantitative and uniform over all the proper solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17066",
  "author_total": 2,
  "authors": [
    {
      "name": "William M Feldman"
    },
    {
      "name": "Inwon C Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nmmvpscj5ghn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17066",
  "fulltext_url": null,
  "id": "2nmmvpscj5ghn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17066",
  "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": "W7213426087",
  "pdf_url": "https://arxiv.org/pdf/2609.17066",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nmmvpscj5ghn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17066",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17066"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Solutions of the Bernoulli one-phase problem with a defect",
  "title_text": "Solutions of the Bernoulli one-phase problem with a defect",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/2nmmvpscj5ghn",
  "venue": "arXiv",
  "versions": []
}