{
  "abstract": "We study positive weak super-solutions of the Lane-Emden inequality $\\mathcal{L}u := \\sum_{i=1}^{n}(-Δ_{p_i})^{s_i}u \\ge u^q$ in $\\mathbb{R}^N$, where each $(-Δ_{p_i})^{s_i}$ is a fractional $p_i$-Laplacian of order $s_i\\in(0,1]$ and exponent $p_i\\in(1,\\infty)$, and $\\max_i s_ip_i<N$. Let $κ_i := (N-s_ip_i)/(p_i-1)$ be the decay exponent of the fundamental solution of the $i$-th operator, and let $\\overlineκ := \\max_iκ_i$. We show that the Serrin exponent of $\\mathcal{L}$ is $\\mathfrak{q}_{\\mathcal{L}} = N/\\overlineκ$. More precisely, for $0<q<\\mathfrak{q}_{\\mathcal{L}}$ the only non-negative continuous weak super-solution is $u\\equiv 0$, while for every $q>\\mathfrak{q}_{\\mathcal{L}}$ we construct explicit positive weak super-solutions of the form $A(λ+|x|)^{-κ}$. In other words, the Serrin exponent of the sum is the smallest of the Serrin exponents $N/κ_i$ of the single operators, that is, the one of the operator whose fundamental solution decays fastest. No structural assumption relating the different operators is needed. The endpoint $q=\\mathfrak{q}_{\\mathcal{L}}$ is left open. The local order $s_i=1$ is treated together with the nonlocal orders, and all the arguments are carried out in the weak setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30415",
  "author_total": 3,
  "authors": [
    {
      "name": "Leandro M. Del Pezzo"
    },
    {
      "name": "Bryan Pichucho"
    },
    {
      "name": "Alexander Quaas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eyvb9famwf17f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30415",
  "fulltext_url": null,
  "id": "eyvb9famwf17f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30415",
  "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": "W7223356938",
  "pdf_url": "https://arxiv.org/pdf/2610.30415",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eyvb9famwf17f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30415",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30415"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Serrin exponent for Lane-Emden inequalities driven by sums of fractional p-Laplacians",
  "title_text": "The Serrin exponent for Lane-Emden inequalities driven by sums of fractional p-Laplacians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/eyvb9famwf17f",
  "venue": "arXiv",
  "versions": []
}