{
  "id": "1307.6578",
  "version": "v2",
  "published": "2013-07-24T20:50:22.000Z",
  "updated": "2014-02-13T14:43:07.000Z",
  "title": "Existence and symmetry for elliptic equations in R^n with arbitrary growth in the gradient",
  "authors": [
    "Lucas C. F. Ferreira",
    "Marcelo Montenegro",
    "Matheus C. Santos"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the semilinear elliptic equation $\\Delta u + g(x,u,Du) = 0$ in $\\R^n$. The nonlinearities $g$ can have arbitrary growth in $u$ and $Du$, including in particular the exponential behavior. No restriction is imposed on the behavior of $g(x,z,p)$ at infinity except in the variable $x$. We obtain a solution $u$ that is locally unique and inherits many of the symmetry properties of $g$. Positivity and asymptotic behavior of the solution are also addressed. Our results can be extended to other domains like half-space and exterior domains. We give some examples.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-13T14:43:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35B06",
      "35B40",
      "35C15",
      "35J91"
    ],
    "keywords": [
      "arbitrary growth",
      "semilinear elliptic equation",
      "exponential behavior",
      "symmetry properties",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6578F"
    }
  }
}