{
  "abstract": "We study normalized ground states for the nonlinear Schrödinger energy on two-dimensional square grids with unbounded defects. We first show that unbounded defects do not necessarily destroy the dimensional crossover, proving its persistence on the half-grid and the quarter-grid. We then consider a prototypical defected grid where a macroscopically two-dimensional region coexists with an unbounded one-dimensional channel. On this graph, normalized ground states do not exist for sufficiently small or sufficiently large masses, showing that the one-dimensional component can dominate the variational problem and induce loss of compactness. Finally, we show that this mechanism is sensitive to the local geometry of the graph: suitable additional defects preserve small-mass nonexistence but restore the existence of ground states for large masses. Our analysis combines small-mass energy asymptotics with a large-mass blow-up argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09908",
  "author_total": 4,
  "authors": [
    {
      "name": "William Borrelli"
    },
    {
      "name": "Nicolò Cangiotti"
    },
    {
      "name": "Simone Dovetta"
    },
    {
      "name": "Lorenzo Tentarelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85cwk2veg3mts.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09908",
  "fulltext_url": null,
  "id": "85cwk2veg3mts",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09908",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7221047158",
  "pdf_url": "https://arxiv.org/pdf/2610.09908",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85cwk2veg3mts.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.09908",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09908"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Normalized nonlinear Schrödinger ground states on defected grids with unbounded defects",
  "title_text": "Normalized nonlinear Schrödinger ground states on defected grids with unbounded defects",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/85cwk2veg3mts",
  "venue": "arXiv",
  "versions": []
}