{
  "abstract": "Continuing the work of the second author (2017), we study the Sobolev critical semilinear elliptic equation in the half-space with an isolated boundary singularity and zero Dirichlet boundary condition. This paper addresses two open questions in this setting: the existence of Delaunay type log-periodic solutions posed by del Pino--Musso--Pacard (2007), and the asymptotic classification of singular solutions posed by Bidaut-Véron--Ponce--Véron (2007). We construct a global continuum of positive log-periodic solutions containing the local bifurcation branch and prove that blow-up along this continuum occurs at a uniquely determined period. We also construct the corresponding concentrating family and prove its local uniqueness. Consequently, the expected stationary asymptotic classification fails, and no universal critical scaling-invariant upper bound can hold throughout the half-space. This behavior contrasts sharply with the classical interior singularity theory of Caffarelli--Gidas--Spruck (1989).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.16106",
  "author_total": 2,
  "authors": [
    {
      "name": "Hua-Yang Wang"
    },
    {
      "name": "Jingang Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mg6rgag2kvyg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.16106",
  "fulltext_url": null,
  "id": "3mg6rgag2kvyg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.16106",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7203718146",
  "pdf_url": "https://arxiv.org/pdf/2608.16106",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mg6rgag2kvyg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2608.16106",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.16106"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Critical Semilinear Elliptic Equation with Isolated Boundary Singularities II",
  "title_text": "The Critical Semilinear Elliptic Equation with Isolated Boundary Singularities II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/3mg6rgag2kvyg",
  "venue": "arXiv",
  "versions": []
}