{
  "id": "1811.06288",
  "version": "v1",
  "published": "2018-11-15T10:44:51.000Z",
  "updated": "2018-11-15T10:44:51.000Z",
  "title": "On $C^1$-approximability of functions by solutions of second order elliptic equations on plane compact sets and $C$-analytic capacity",
  "authors": [
    "Petr V. Paramonov",
    "Xavier Tolsa"
  ],
  "categories": [
    "math.CA",
    "math.AP"
  ],
  "abstract": "Criteria for approximability of functions by solutions of homogeneous second order elliptic equations (with constant complex coefficients) in the norms of the Whitney $C^1$-spaces on compact sets in $\\mathbb R^2$ are obtained in terms of the respective $C^1$-capacities. It is proved that the mentioned $C^1$-capacities are comparable to the classic $C$-analytic capacity, and so have a proper geometric measure characterization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-15T10:44:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30E10",
      "31A35",
      "35B60",
      "35J15"
    ],
    "keywords": [
      "plane compact sets",
      "analytic capacity",
      "approximability",
      "homogeneous second order elliptic equations",
      "proper geometric measure characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}