{
  "abstract": "In this work, we establishes results of existence and regularity for solutions to nonlocal equations of the form $f(Δ)u = U(x,u(x)) ~\\text{and}~f(Δ_{g})u=U(x,u(x))$ in the Euclidean context and Riemannian context respectively. We extend the results of \\cite{Gorka 6} for the Euclidean space $\\mathbb{R}^{n}$ under cylindrically symmetry and compact Riemannian manifolds $(M,g)$ under action of a closed Lie subgroup $G \\leq \\text{Isom}_{g}(M)$. Our approach combines spectral theory, complex interpolation and fixed-point methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28546",
  "author_total": 1,
  "authors": [
    {
      "name": "Santiago Castellanos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72h06rvxddepm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28546",
  "fulltext_url": null,
  "id": "72h06rvxddepm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28546",
  "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": "W7223117422",
  "pdf_url": "https://arxiv.org/pdf/2610.28546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72h06rvxddepm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On Nonlocal Equations under Symmetries",
  "title_text": "On Nonlocal Equations under Symmetries",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/72h06rvxddepm",
  "venue": "arXiv",
  "versions": []
}