{
  "abstract": "Let $T$ be a nonhomogeneous rooted tree equipped with a positive flow measure $m$. For $1<p<\\infty$, consider the variable-coefficient Sobolev space on the nonhomogeneous flow-measure tree~$T$ \\[ W_a^{1,p}(T,m) = \\left\\{ f\\in L^p(T,m): \\sum_{x\\ne ρ}a(x)m(x)\\lvert f(x)-f(π(x))\\rvert^p<\\infty \\right\\}, \\] where $a$ is a positive variable coefficient, $ρ$ denotes the root and $π(x)$ denotes the parent of $x$. Using an averaging method over descendant levels, we prove the density of finitely supported functions in $W_a^{1,p}(T,m)$ for coefficients satisfying a weighted moment condition. As an application, the relationship between solutions on finite domains and global solutions is clarified for $p=2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07350",
  "author_total": 3,
  "authors": [
    {
      "name": "Zeyu Cheng"
    },
    {
      "name": "Yichun Zhao"
    },
    {
      "name": "Jiang Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bxh71ct3emds4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07350",
  "fulltext_url": null,
  "id": "bxh71ct3emds4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07350",
  "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/2611.07350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bxh71ct3emds4.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Finite-Support Approximation in Variable-Coefficient Sobolev Spaces on Nonhomogeneous Flow-Measure Trees",
  "title_text": "Finite-Support Approximation in Variable-Coefficient Sobolev Spaces on Nonhomogeneous Flow-Measure Trees",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:34Z",
  "url": "https://research.draconitic.com/paper/bxh71ct3emds4",
  "venue": "arXiv",
  "versions": []
}