{
  "abstract": "Let \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega \\subset {\\mathbb {R}}^{n+1}$$\\end{document}Ω⊂Rn+1 be a bounded chord-arc domain, let \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}=-\\textrm{div} A\\nabla $$\\end{document}L=-divA∇ be an elliptic operator in Ω Ω associated with a matrix A having Dini mean oscillation coefficients, and let 1<p≤ 21<p≤2. In this paper we show that if the regularity problem for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}$$\\end{document}L is solvable in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^q$$\\end{document}Lq for some q>pq>p in Ω Ω, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\partial \\Omega }$$\\end{document}∂Ω supports a weak p-Poincaré inequality, and Ω Ω has very big pieces of superdomains for which the Neumann problem for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}$$\\end{document}L is solvable uniformly in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^q$$\\end{document}Lq, then the Neumann problem for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}$$\\end{document}L is solvable in \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}Lp in Ω Ω.",
  "abstract_shown": true,
  "affiliations": [
    "Departamento de Matemáticas, Universidad del País Vasco, UPV/EHU, Barrio Sarriena s/n, 48940 Leioa, Spain",
    "Ikerbasque, Basque Foundation for Science, Bilbao, Spain",
    "ICREA, Barcelona, Dept. de Matemàtiques, Universitat Autònoma de Barcelona, and Centre de Recerca Matemàtica, Barcelona, Catalonia Spain"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Mihalis Mourgoglou",
      "orcid": "0000-0002-9634-6713"
    },
    {
      "affs": [
        2
      ],
      "name": "Xavier Tolsa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ad8hyyq52yn3y.bib",
  "cited_by": 1,
  "doi": "10.1007/s00205-026-02236-x",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13724656/",
  "id": "ad8hyyq52yn3y",
  "issns": [
    "0003-9527",
    "1432-0673"
  ],
  "landing_url": "https://doi.org/10.1007/s00205-026-02236-x",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "Article"
    ],
    [
      "openalex",
      "2604|Advanced Harmonic Analysis Research"
    ]
  ],
  "openalex": "W4401202798",
  "pdf_url": "https://europepmc.org/articles/PMC13724656?pdf=render",
  "pmcid": "PMC13724656",
  "pmid": "42973891",
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ad8hyyq52yn3y.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:23:11Z",
      "native_id": "PMC13724656",
      "source": "pmc",
      "url": "https://doi.org/10.1007/s00205-026-02236-x"
    },
    {
      "first_seen": "2026-11-04T15:20:47Z",
      "native_id": "MED:42973891",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42973891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Advanced Harmonic Analysis Research",
      "subfield": "general"
    }
  ],
  "title": "Solvability of the Neumann Problem for Elliptic Equations in Chord-Arc Domains with Very Big Pieces of Good Superdomains",
  "title_text": "Solvability of the Neumann Problem for Elliptic Equations in Chord-Arc Domains with Very Big Pieces of Good Superdomains",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T12:21:05Z",
  "url": "https://research.draconitic.com/paper/ad8hyyq52yn3y",
  "venue": "Archive for Rational Mechanics and Analysis",
  "versions": []
}