{
  "abstract": "We establish a frequency localized maximum principle for parabolic second-order partial differential equations with the Caputo time fractional derivative $\\partial_t^α$ of order $α\\in(0,1)$. The leading coefficients are uniformly elliptic, measurable in time, and independent of space. We construct suitable equivalent norms on frequency localized subspaces of $L_\\infty(\\mathbb{R}^d)$, for which a frequency localized maximum principle holds. The corresponding result may fail in the usual $L_\\infty$ norm even for the classical heat equation. As an application, we prove existence, uniqueness, and regularity estimates in Sobolev-Zygmund spaces with Muckenhoupt weights in time for equations with spatially variable coefficients and zero initial data. The coefficients are strongly measurable in time with values in a Hölder-Zygmund space of positive order and uniformly bounded in this space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24476",
  "author_total": 2,
  "authors": [
    {
      "name": "Jae-Hwan Choi"
    },
    {
      "name": "Junhee Ryu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7hb4bgn72t8j3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24476",
  "fulltext_url": null,
  "id": "7hb4bgn72t8j3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24476",
  "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"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7223024377",
  "pdf_url": "https://arxiv.org/pdf/2610.24476",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7hb4bgn72t8j3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24476",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24476"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A frequency localized maximum principle and its applications to time fractional equations with rough coefficients",
  "title_text": "A frequency localized maximum principle and its applications to time fractional equations with rough coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7hb4bgn72t8j3",
  "venue": "arXiv",
  "versions": []
}