{
  "abstract": "We study a fractional Brezis--Nirenberg problem on a bounded domain with finitely many Hardy potentials centered at distinct points $a_1,\\dots,a_k$, with masses $μ_1,\\dots,μ_k\\geq 0$. We assume $\\sum_{i=1}^kμ_i<Λ_{N,s}$ and consider $N>4s$ and $0<μ_{\\max}<\\overlineμ_{N,s}$. The interaction between the poles allows existence for $λ=0$ and for some negative values of $λ$. At a pole $a_j$, this interaction is described by $B_j(λ,\\mathbf a,\\boldsymbolμ)=λ+\\sum_{i\\neq j}\\frac{μ_i}{|a_i-a_j|^{2s}}$. This leads to a threshold $λ_{\\mathrm{geo}}\\leq 0$. We prove that the critical Rayleigh quotient is attained for $λ_{\\mathrm{geo}}<λ<λ_1(\\boldsymbolμ,\\mathbf a)$, and hence the problem admits a positive least-energy solution. If at least two masses are positive, then $λ_{\\mathrm{geo}}<0$, so the result includes $λ=0$ and a nonempty interval of negative values of $λ$. We also prove a direct compactness estimate for weakly vanishing sequences by localizing the Gagliardo seminorm. The argument avoids both profile decomposition and the Caffarelli-Silvestre extension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22877",
  "author_total": 1,
  "authors": [
    {
      "name": "Debangana Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7dj38q04qvwc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22877",
  "fulltext_url": null,
  "id": "d7dj38q04qvwc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22877",
  "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": "W7214027652",
  "pdf_url": "https://arxiv.org/pdf/2609.22877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7dj38q04qvwc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A fractional Brezis-Nirenberg problem with multipolar Hardy potentials",
  "title_text": "A fractional Brezis-Nirenberg problem with multipolar Hardy potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/d7dj38q04qvwc",
  "venue": "arXiv",
  "versions": []
}