{
  "id": "math/0701344",
  "version": "v2",
  "published": "2007-01-12T13:30:52.000Z",
  "updated": "2007-01-30T16:30:06.000Z",
  "title": "Fundamental solutions in the Colombeau framework: applications to solvability and regularity theory",
  "authors": [
    "Claudia Garetto"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we introduce the notion of fundamental solution in the Colombeau context as an element of the dual $\\LL(\\Gc(\\R^n),\\wt{\\C})$. After having proved the existence of a fundamental solution for a large class of partial differential operators with constant Colombeau coefficients, we investigate the relationships between fundamental solutions in $\\LL(\\Gc(\\R^n),\\wt{\\C})$, Colombeau solvability and $\\G$- and $\\Ginf$-hypoellipticity respectively.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-30T16:30:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46F30",
      "35E05"
    ],
    "keywords": [
      "fundamental solution",
      "colombeau framework",
      "regularity theory",
      "applications",
      "partial differential operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1344G"
    }
  }
}