{
  "id": "2204.13934",
  "version": "v1",
  "published": "2022-04-29T08:20:57.000Z",
  "updated": "2022-04-29T08:20:57.000Z",
  "title": "Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena",
  "authors": [
    "Pu-Zhao Kow",
    "Simon Larson",
    "Mikko Salo",
    "Henrik Shahgholian"
  ],
  "comment": "42 pages, 6 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering problems, and show that there are non-scattering domains for the Helmholtz equation at any positive frequency that have inward cusps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-29T08:20:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J05",
      "35J15",
      "35J20",
      "35R30",
      "35R35"
    ],
    "keywords": [
      "helmholtz equation",
      "quadrature domains",
      "non-scattering phenomena",
      "application",
      "partial balayage procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}