{
  "abstract": "In this article, we study unique continuation properties at infinity for solutions to generalized Schrödinger equations with potential functions that belong to the reverse Hölder class. For equations of the form $-div (A \\nabla u) + V u = 0$ in $\\mathbb{R}^n$, where $A$ is bounded and elliptic and $V \\in RH_p$ for some $p \\in [\\frac n 2, \\infty]$, we prove that if a solution doesn't grow too quickly at infinity, then it must be trivial. We use $d_V$, the Agmon distance function associated to $V$, to quantify the threshold growth rate. More precisely, there exists a constant $γ_0 > 0$ so that if $|u(x)| \\lesssim \\exp(γd_V(x, 0))$ for some $γ< γ_0$ and every $x \\in \\mathbb{R}^n$, then $u$ must be trivial. The result may be interpreted as a Liouville-type theorem and is related to Landis' conjecture. Our proof techniques are inspired by Z. Shen's exponential decay estimates for fundamental solutions of Schrödinger operators and involve the application of a Fefferman-Phong inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21048",
  "author_total": 1,
  "authors": [
    {
      "name": "Blair Davey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8e3y57k55xr06.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21048",
  "fulltext_url": null,
  "id": "8e3y57k55xr06",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21048",
  "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",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7213933397",
  "pdf_url": "https://arxiv.org/pdf/2609.21048",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8e3y57k55xr06.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21048",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21048"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Unique continuation at infinity for Schrödinger equations with Reverse Hölder Potentials",
  "title_text": "Unique continuation at infinity for Schrödinger equations with Reverse Hölder Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/8e3y57k55xr06",
  "venue": "arXiv",
  "versions": []
}