{
  "abstract": "Let $k\\ge2$ be an integer. We prove that every minimizer of the Bethuel--Brezis--Coron relaxed Dirichlet energy in the signed meridional $k$-axial class, with continuous $H^1$ degree-zero data on the boundary of a ball, is smooth outside a finite subset of the symmetry axis. This extends the weight-one finiteness theorem of Hardt--Lin--Poon and resolves the finite-singularity question posed by Martinazzi--Rivière as Open Problem~A, in the fixed-boundary Bethuel--Brezis--Coron setting with continuous degree-zero data. The interior argument uses a distributional graph-boundary identity, height-preserving half-turn replacements, and exact square completions retaining the current cost. Cap-valued crosscuts and a finite incidence count exclude singular accumulation at the boundary poles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07414",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhiyuan Dai"
    },
    {
      "name": "Huaijie Wang"
    },
    {
      "name": "Wei Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2e9sfavrmq017.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07414",
  "fulltext_url": null,
  "id": "2e9sfavrmq017",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07414",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07414",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2e9sfavrmq017.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07414",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07414"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finiteness of singularities for higher-weight axially symmetric minimizers of the relaxed Dirichlet energy",
  "title_text": "Finiteness of singularities for higher-weight axially symmetric minimizers of the relaxed Dirichlet energy",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:34Z",
  "url": "https://research.draconitic.com/paper/2e9sfavrmq017",
  "venue": "arXiv",
  "versions": []
}