{
  "id": "1403.1538",
  "version": "v3",
  "published": "2014-03-06T19:33:13.000Z",
  "updated": "2014-04-08T13:57:27.000Z",
  "title": "Energy estimates for minimizers to a class of elliptic systems of Allen-Cahn type and the Liouville property",
  "authors": [
    "Christos Sourdis"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove a theorem for the growth of the energy of bounded, globally minimizing solutions to a class of semilinear elliptic systems of the form $\\Delta u=\\nabla W(u)$, $x\\in \\mathbb{R}^n$, $n\\geq 2$, with $W:\\mathbb{R}^m\\to \\mathbb{R}$, $m\\geq 1$, nonnegative and vanishing at exactly one point (at least in the closure of the image of the considered solution $u$). As an application, we can prove a Liouville type theorem under various assumptions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-08T13:57:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy estimates",
      "allen-cahn type",
      "liouville property",
      "minimizers",
      "semilinear elliptic systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.1538S"
    }
  }
}