{
  "abstract": "We prove the existence of optimizers for a class of homogeneous Gagliardo-Nirenberg inequalities of the form $$ \\|D^{s}ϕ\\|_{L^q} \\leq C \\|D^{s_1}ϕ\\|_{L^p}^{1-θ} \\|D^{s_2}ϕ\\|_{L^2}^θ, \\quad s_1<s_2, $$ under the scaling relation $$ \\frac{1}{q}-\\frac{s}{d} = (1-θ)\\left(\\frac{1}{p}-\\frac{s_1}{d}\\right) + θ\\left(\\frac{1}{2}-\\frac{s_2}{d}\\right), $$ and the strict interpolation condition $$ s<(1-θ)s_1+θs_2. $$ When $s>s_1$, the problem reduces, after shifting the derivative orders, to the result of Bellazzini, Frank and Visciglia, whereas the case $s\\leq s_1$ follows from the present paper. As an application, we study normalized solutions of the associated Euler-Lagrange equations under the constraint $$ \\|D^{s_1}ψ\\|_{L^p}^p=λ>0. $$ In particular, the case $p=2$ includes the stationary equation arising from the Majda-McLaughlin-Tabak (MMT) model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08686",
  "author_total": 2,
  "authors": [
    {
      "name": "Amin Esfahani"
    },
    {
      "name": "Mukhtar Karazym"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6wsswmj94aha3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08686",
  "fulltext_url": null,
  "id": "6wsswmj94aha3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08686",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7202192539",
  "pdf_url": "https://arxiv.org/pdf/2608.08686",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6wsswmj94aha3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2608.08686",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08686"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp homogeneous Gagliardo--Nirenberg inequalities and normalized solutions for generalized stationary MMT equations",
  "title_text": "Sharp homogeneous Gagliardo--Nirenberg inequalities and normalized solutions for generalized stationary MMT equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/6wsswmj94aha3",
  "venue": "arXiv",
  "versions": []
}