{
  "abstract": "We study attainment of the best constant in \\begin{equation*} \\int_{\\mathbb R^{m+n}} \\bigl(|\\nabla_xu|^2+|x|^2|\\nabla_yu|^2+a|u|^2\\bigr) \\geq S_a\\left(\\int_{\\mathbb R^{m+n}} (1+|x|^2)^{n/(Q-2)}|u|^q\\right)^{2/q}, \\end{equation*} where \\(m,n\\geq1\\), \\(Q=m+2n\\), \\(q=2Q/(Q-2)\\), and \\(a>0\\). Using annular interpolation and a transverse-average recurrence with \\(L^q\\) contraction \\(2^{-m/q}\\), we decompose bounded sequences into finite, Grushin and Euclidean profiles. Energy and critical mass split, with a power bound in the number of profiles on the remaining mass. We prove compactness of normalized minimizing sequences modulo \\(y\\)-translations under \\(S_a<\\min\\{S_G,a^{n/Q}S_E(1)\\}\\), where \\(S_G\\) and \\(S_E(1)\\) are the tangent constants. The strict-binding set is empty or an open interval; we prove nonemptiness for \\(n=1\\) and even \\(m\\geq6\\). At finite positive endpoints of a nonempty binding interval, we characterize attainment by first-order binding gaps. We obtain a finite critical-profile decomposition of Palais--Smale sequences with a remainder vanishing in energy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01094",
  "author_total": 2,
  "authors": [
    {
      "name": "Shengbing Deng"
    },
    {
      "name": "Dehong Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zwwtw5pnr1w2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01094",
  "fulltext_url": null,
  "id": "1zwwtw5pnr1w2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01094",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zwwtw5pnr1w2.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01094"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Profile decomposition, strict binding and global compactness for a critical Grushin embedding",
  "title_text": "Profile decomposition, strict binding and global compactness for a critical Grushin embedding",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/1zwwtw5pnr1w2",
  "venue": "arXiv",
  "versions": []
}