{
  "abstract": "Motivated by the pressure formation problem for hydrodynamic models with nonlocal interactions, we classify strong Lebesgue lower bounds for the Riesz energy functional and for a determinant functional arising from the theory of compensated integrability. The classification covers all integrability exponents in $(0,\\infty]$ within the class of confined log-concave densities. These geometric assumptions are motivated by counterexamples for general densities. On the whole space, neither functional controls any fixed Lebesgue quasi-norm. Under confinement, lower bounds fail for exponents greater than one, whereas $L^1$ bounds hold for the energy in every dimension and for the determinant only in dimension one. The log-concave estimates hold at sharp integrability exponents and follow from endpoint Lorentz bounds for confined quasiconcave densities and a weak-to-strong lemma. In particular, the energy estimates provide a geometric lower-bound counterpart to the classical Hardy-Littlewood-Sobolev inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03215",
  "author_total": 2,
  "authors": [
    {
      "name": "Nuno J. Alves"
    },
    {
      "name": "Athanasios E. Tzavaras"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1q2sm5bwb1wxn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03215",
  "fulltext_url": null,
  "id": "1q2sm5bwb1wxn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03215",
  "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.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03215",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1q2sm5bwb1wxn.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03215",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03215"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lower bounds for Riesz interaction functionals",
  "title_text": "Lower bounds for Riesz interaction functionals",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/1q2sm5bwb1wxn",
  "venue": "arXiv",
  "versions": []
}