{
  "abstract": "We develop the mathematical analysis of the Time-Dependent Density Functional Theory introduced by Manfredi [J. Plasma Phys., 86.2 (2020), 825860201] in the setting of Vlasov equations with a time-dependent exterior potential. In this context, we establish the invertibility of the potential-density mapping for the Vlasov-Poisson system on $\\mathbb{T}^d \\times \\mathbb{R}^d$ when the exterior potential is (real-)analytic in the space variable. We also recover a Runge-Gross type Theorem for the Vlasov-Poisson equation for smooth (real-)analytic in time exterior potential. The surjectivity of the potential-density mapping is an inverse problem for the Vlasov-Poisson equation: we find the electric field that generates a given density profile on a given time interval.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08586",
  "author_total": 1,
  "authors": [
    {
      "name": "Simon Le Bouëdec"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/49720fzzz0h8n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08586",
  "fulltext_url": null,
  "id": "49720fzzz0h8n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08586",
  "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",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7212084260",
  "pdf_url": "https://arxiv.org/pdf/2609.08586",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/49720fzzz0h8n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08586",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08586"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the Invertibility of the Potential-Density Mapping for the Vlasov-Poisson System in Analytic Spaces",
  "title_text": "On the Invertibility of the Potential-Density Mapping for the Vlasov-Poisson System in Analytic Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/49720fzzz0h8n",
  "venue": "arXiv",
  "versions": []
}