{
  "abstract": "We establish Morrey-type conditions ensuring that a finite signed Radon measure belongs to the dual of the energy space of solutions to nonlinear parabolic equations of $p$-Laplacian type. More precisely, for the parabolic cylinders $Q_{r,r^p}(z):=B_r(x)\\times(t-r^p,t+r^p)$, we prove that \\[ |μ|\\bigl(Q_{r,r^p}(z)\\cap(Ω\\times (0,T))\\bigr) \\leq Mr^{n+p-\\vartheta}, \\qquad \\vartheta<p, \\] implies duality, and this threshold is sharp in general. More generally, for cylinders with time length proportional to $r^q$, $q>1$, the sufficient threshold is $\\vartheta<\\min\\{p,q\\}$. Finally, we discuss the resulting variational, energy, and renormalized solution theories for nonlinear parabolic equations with measure data, relating our conclusions to the existing literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32646",
  "author_total": 1,
  "authors": [
    {
      "name": "Lorenzo Braglia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvgzdx7dx7e4h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32646",
  "fulltext_url": null,
  "id": "dvgzdx7dx7e4h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32646",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7214713940",
  "pdf_url": "https://arxiv.org/pdf/2609.32646",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvgzdx7dx7e4h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32646",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32646"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Duality Conditions for Morrey Measures via Parabolic Capacity",
  "title_text": "Duality Conditions for Morrey Measures via Parabolic Capacity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/dvgzdx7dx7e4h",
  "venue": "arXiv",
  "versions": []
}