{
  "abstract": "Let $X$ be a time-homogeneous one-dimensional diffusion whose coefficients satisfy the Engelbert--Schmidt conditions, and let $q$ be a bounded potential. We show that the associated Feynman--Kac semigroup is smooth in time and $C^1$ in space, with a locally absolutely continuous first spatial derivative; the Kolmogorov equation holds almost everywhere. If the drift, second-order coefficient, and potential are continuous, the Feynman--Kac value is $C^{1,2}$ in the interior. Thus, in the time-homogeneous one-dimensional setting, continuity suffices for interior $C^{1,2}$ regularity. We identify the corresponding semigroups with the killed and reflected Feynman--Kac functionals, treat nonzero, time-independent Dirichlet data, and give examples showing the sharpness of the continuity assumptions and the failure of the corresponding statement in two dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29854",
  "author_total": 1,
  "authors": [
    {
      "name": "Johannes Ruf"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8paqgr39m71y5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29854",
  "fulltext_url": null,
  "id": "8paqgr39m71y5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29854",
  "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"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7204925058",
  "pdf_url": "https://arxiv.org/pdf/2608.29854",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8paqgr39m71y5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29854",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29854"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "One-dimensional Feynman--Kac regularity under the Engelbert--Schmidt conditions",
  "title_text": "One-dimensional Feynman--Kac regularity under the Engelbert--Schmidt conditions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/8paqgr39m71y5",
  "venue": "arXiv",
  "versions": []
}