{
  "id": "1908.10257",
  "version": "v1",
  "published": "2019-08-27T15:04:29.000Z",
  "updated": "2019-08-27T15:04:29.000Z",
  "title": "Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators",
  "authors": [
    "Stefano Biagi",
    "Ermanno Lanconelli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Maximum Principles on unbounded domains play a crucial r\\^ole in several problems related to linear second-order PDEs of elliptic and parabolic type. In this paper we consider a class of sub-elliptic operators $\\mathcal{L}$ in $\\mathbb{R}^N$ and we establish some criteria for an unbounded open set to be a Maximum Principle set for $\\mathcal{L}$. We extend some classical results related to the Laplacian (by Deny, Hayman and Kennedy) and to the sub-Laplacians on stratified Lie groups (by Bonfiglioli and the second-named author).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-27T15:04:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B50",
      "35J70",
      "31C05"
    ],
    "keywords": [
      "sub-elliptic operators",
      "large sets",
      "linear second-order pdes",
      "maximum principle set",
      "parabolic type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}