{
  "abstract": "We construct singular weak solutions to scalar, linear, uniformly parabolic equations with complex coefficients in one space dimension. Our examples show that the space-time integrability provided by the energy estimates is sharp: for every $p>6$, there exists such an equation admitting an energy solution that fails to be $p$-integrable on a compact subset of the space-time domain. In particular, the local boundedness of weak solutions from the De Giorgi--Nash--Moser theory fails for complex coefficients already in one space dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17351",
  "author_total": 3,
  "authors": [
    {
      "name": "Pascal Auscher"
    },
    {
      "name": "Moritz Egert"
    },
    {
      "name": "Benjamin W. Kosmala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9ajawd7d8s0h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17351",
  "fulltext_url": null,
  "id": "a9ajawd7d8s0h",
  "issns": [],
  "landing_url": "https://hal.science/hal-05739311v1",
  "language": "en",
  "licence": "CC-BY-NC-4.0",
  "licence_label": "CC BY-NC 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
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      "arxiv",
      "math.CA"
    ],
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      "hal",
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    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
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  "openalex": "W7213438486",
  "pdf_url": "https://hal.science/hal-05739311/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9ajawd7d8s0h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:29Z",
      "native_id": "hal-05739311",
      "source": "hal",
      "url": "https://hal.science/hal-05739311v1"
    },
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "SINGULAR SOLUTIONS TO PARABOLIC EQUATIONS IN ONE SPACE DIMENSION",
  "title_text": "SINGULAR SOLUTIONS TO PARABOLIC EQUATIONS IN ONE SPACE DIMENSION",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/a9ajawd7d8s0h",
  "venue": "HAL",
  "versions": []
}