{
  "abstract": "This article aims at solving open questions related to the well-posedness of Potential theory objects in a hypoelliptic setting. We provide here the expression of the equilibrium measure, capacity and electrostatic energy between smooth open sets $\\A$ and $\\B$ for the underdamped Langevin process. Additionally, the capacity is shown to be the solution of two variational principles which extend the well-known Dirichlet and Thomson principles in the hypoelliptic setting. Due to the degeneracy of the operator at hand, the results display significant differences with the standard elliptic setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21781",
  "author_total": 1,
  "authors": [
    {
      "name": "Mouad Ramil"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kssfcxtmaemd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21781",
  "fulltext_url": null,
  "id": "6kssfcxtmaemd",
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  "landing_url": "https://hal.science/hal-05802116v1",
  "language": "en",
  "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"
    ],
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      "hal",
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    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  "openalex": "W7222725707",
  "pdf_url": "https://arxiv.org/pdf/2610.21781",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kssfcxtmaemd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05802116",
      "source": "hal",
      "url": "https://hal.science/hal-05802116v1"
    },
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21781",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21781"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Fundamentals of Potential theory for a hypoelliptic process",
  "title_text": "Fundamentals of Potential theory for a hypoelliptic process",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/6kssfcxtmaemd",
  "venue": "HAL",
  "versions": []
}