{
  "abstract": "Let $Ω\\subset\\mathbb R^2$ be a bounded smooth domain. We prove that the weak Dirichlet-to-Neumann map for $-Δ+V$ uniquely determines every complex-valued potential $V\\in L^p(Ω)$, $p>1$, provided that zero is not a Dirichlet eigenvalue. This extends the previously known range $p>4/3$ to all $p>1$. The proof uses Bukhgeim's quadratic-phase solutions and an average of Alessandrini's identity over the phase center. After separating the Neumann-series tails, we show that each remaining Born term tends to zero. The fixed-order estimates combine bounds for the absolute kernels with oscillatory cancellation and a duality argument for the product of the two Cauchy transforms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28046",
  "author_total": 2,
  "authors": [
    {
      "name": "Cătălin I. Cârstea"
    },
    {
      "name": "Jenn-Nan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e9mw8ty161cj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28046",
  "fulltext_url": null,
  "id": "e9mw8ty161cj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28046",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7214239474",
  "pdf_url": "https://arxiv.org/pdf/2609.28046",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e9mw8ty161cj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28046",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28046"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Uniqueness for the inverse Schrödinger problem in the plane with $L^p$ potentials, $p>1$",
  "title_text": "Uniqueness for the inverse Schrödinger problem in the plane with L^p potentials, p>1",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/e9mw8ty161cj7",
  "venue": "arXiv",
  "versions": []
}