{
  "abstract": "We fully describe the set of regular and irregular boundary points for a general hypoelliptic stochastic process $(X(t))_{t\\geq0}$ absorbed outside a $C^{3,\\,1}$ domain $Ω$. The well-posedness of the associated boundary-value problem on $Ω$ is also established in the classical sense. Let us emphasize that, throughout this work, no assumption is made regarding the inherent structure of the boundary of $Ω$. In particular, characteristic and non-characteristic points may coexist on $\\partialΩ$, thus extending previous results obtained in the literature. We show that, unlike previous settings, the solution to this boundary-value problem may exhibit discontinuity at the boundary $\\partialΩ$. In certain cases involving a $C^\\infty$ domain $Ω$ and $C^\\infty$ coefficients, the discontinuity set is even of positive Lebesgue surface measure on $\\partialΩ$. Finally, we highlight a cone condition under which the continuity is preserved at the boundary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39409",
  "author_total": 2,
  "authors": [
    {
      "name": "Mouad Ramil"
    },
    {
      "name": "Mathias Rousset"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7nxx6j1g8rk23.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39409",
  "fulltext_url": null,
  "id": "7nxx6j1g8rk23",
  "issns": [],
  "landing_url": "https://inria.hal.science/hal-05773317v1",
  "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.PR"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2604|Differential Equations and Boundary Problems"
    ]
  ],
  "openalex": "W7215032081",
  "pdf_url": "https://arxiv.org/pdf/2609.39409",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7nxx6j1g8rk23.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:45Z",
      "native_id": "hal-05773317",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05773317v1"
    },
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39409",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39409"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Regular points and the boundary-value problem for a hypoelliptic process in a general smooth domain",
  "title_text": "Regular points and the boundary-value problem for a hypoelliptic process in a general smooth domain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/7nxx6j1g8rk23",
  "venue": "HAL",
  "versions": []
}