{
  "id": "1405.1541",
  "version": "v1",
  "published": "2014-05-07T09:25:25.000Z",
  "updated": "2014-05-07T09:25:25.000Z",
  "title": "On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in ${\\bf R}^2$",
  "authors": [
    "Giorgio Fusco",
    "Francesco Leonetti",
    "Cristina Pignotti"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain $\\Omega\\subset {\\bf R}^n.$ Under suitable assumptions, we prove an existence result and a uniform exponential estimate for symmetric solutions. In dimension n=2 an additional asymptotic result is obtained. These results are based on a pointwise estimate obtained for local minimizers of the Allen-Cahn energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-07T09:25:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric solutions",
      "allen-cahn equation",
      "asymptotic behavior",
      "unbounded domains",
      "additional asymptotic result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.1541F"
    }
  }
}