{
  "abstract": "We study an unbalanced optimal transport problem with a spatially independent signed source. The target density is continuous on a bounded domain or continuous and integrable on $\\mathbb R^n$. We establish sequential weak lower semicontinuity at the critical Sobolev regularity $W^{1,n}$ and existence of minimizers under prescribed distortion and Jacobian mass bounds, provided a finite-energy admissible pair exists. For domain-preserving, uniformly bi-Lipschitz affine flows, we prove an energy-preserving static-dynamic correspondence and stability of the reconstruction. Within this class, sequential $Γ$-convergence identifies the strong source-penalty limit as transport minimization among pairs of minimum source cost. This yields optimal-cost asymptotics and subsequential convergence of minimizers and their reconstructed paths. When a constant source is admissible, optimal sources converge strongly in $L^2$ to the constant determined by the endpoint mass difference. We establish local constant-source feasibility for Hölder endpoint densities near a fixed reference pair and give a quantitative obstruction showing that constant-source feasibility may fail even when admissible pairs exist.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41321",
  "author_total": 2,
  "authors": [
    {
      "name": "Qing Zhao"
    },
    {
      "name": "Feida Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c52aqehvgn1b7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41321",
  "fulltext_url": null,
  "id": "c52aqehvgn1b7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41321",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41321",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c52aqehvgn1b7.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41321",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41321"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Existence, Equivalence, and Convergence of Unbalanced Optimal Transport",
  "title_text": "Existence, Equivalence, and Convergence of Unbalanced Optimal Transport",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/c52aqehvgn1b7",
  "venue": "arXiv",
  "versions": []
}