{
  "id": "2307.11219",
  "version": "v1",
  "published": "2023-07-20T20:17:48.000Z",
  "updated": "2023-07-20T20:17:48.000Z",
  "title": "Approximation of functions on a compact set by solutions of elliptic equations. Quantitative results",
  "authors": [
    "Grigori Rozenblum",
    "Nikolai Shirokov"
  ],
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We establish that a generalized H\\\"{o}lder continuous function on an $(m-2)$-Ahlfors regular compact set in $\\mathbb{R}^m$ can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-20T20:17:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A30",
      "35J15",
      "41A25"
    ],
    "keywords": [
      "elliptic equation",
      "quantitative results",
      "approximation",
      "ahlfors regular compact set",
      "continuity modulus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}