{
  "abstract": "We prove the Aleksandrov-Bakelman-Pucci maximum principle for $L^n$-viscosity sub/super-solutions of fully nonlinear uniformly elliptic equations in $Ω\\subset\\mathbb R^n$ with the drift coefficient $γ$ such that $γ(\\ln(1+γ))^{\\frac{n-1}{n}}\\in L^n(Ω)$. The approach is based on convex duality and Trudinger-Moser type inequalities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03918",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrzej Święch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4g11hvmwqxa3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03918",
  "fulltext_url": null,
  "id": "4g11hvmwqxa3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03918",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220651596",
  "pdf_url": "https://arxiv.org/pdf/2610.03918",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g11hvmwqxa3c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03918",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03918"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Aleksandrov-Bakelman-Pucci maximum principle for $L^n$-viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case",
  "title_text": "Aleksandrov-Bakelman-Pucci maximum principle for L^n-viscosity solutions of uniformly elliptic equations with unbounded terms: The critical case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4g11hvmwqxa3c",
  "venue": "arXiv",
  "versions": []
}