{
  "abstract": "Inverse source problems in divergence form consist in finding a vector field with prescribed support S, whose divergence is the Laplacian of some observed potential. In this paper, we assume the unknown vector field is a vector-valued measure, and we study the corresponding least square inversion problems, regularized by penalizing the total variation, without discretizing the criterion nor the unknown. We prove that this problem has a unique minimizer in the case where S is a slender set; i.e., it has zero Lebesgue measure and each connected component of its complement has infinite Lebesgue measure. The proof relies on a refinement of Smirnov's decomposition of divergence-free measures [62] which is of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11719",
  "author_total": 3,
  "authors": [
    {
      "name": "L Baratchart"
    },
    {
      "name": "D P Hardin"
    },
    {
      "name": "C Villalobos-Guillén"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bcxd7144z9gss.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11719",
  "fulltext_url": null,
  "id": "bcxd7144z9gss",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11719",
  "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",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7221162024",
  "pdf_url": "https://arxiv.org/pdf/2610.11719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bcxd7144z9gss.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.11719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11719"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness for tv-regularized inverse problems with source in divergence form",
  "title_text": "Uniqueness for tv-regularized inverse problems with source in divergence form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/bcxd7144z9gss",
  "venue": "arXiv",
  "versions": []
}