{
  "id": "1503.01801",
  "version": "v1",
  "published": "2015-03-05T22:06:18.000Z",
  "updated": "2015-03-05T22:06:18.000Z",
  "title": "Weighted ${L^p}$-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups",
  "authors": [
    "Andrea Bonfiglioli",
    "Alessia E. Kogoj"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\\mathcal{L}$ on Lie groups $\\mathbb{G}$ whose underlying manifold is $n$-dimensional space. We show that a natural weight is the right-invariant measure $\\check{H}$ of $\\mathbb{G}$. We also prove Liouville-type theorems for $C^2$ subsolutions in $L^p(\\mathbb{G},\\check{H})$. We provide examples of operators to which our results apply, jointly with an application to the uniqueness for the Cauchy problem for the evolution operator $\\mathcal{L}-\\partial_t$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-05T22:06:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B53",
      "35H10",
      "35R03",
      "35H20",
      "35J70"
    ],
    "keywords": [
      "liouville theorems",
      "lie groups",
      "order hypoelliptic partial differential operators",
      "second order hypoelliptic partial differential",
      "natural weight"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}