{
  "id": "0904.1828",
  "version": "v1",
  "published": "2009-04-11T23:21:06.000Z",
  "updated": "2009-04-11T23:21:06.000Z",
  "title": "Periodic unfolding and homogenization for the Ginzburg-Landau Equation",
  "authors": [
    "Myrto Sauvageot"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate, on a bounded domain $\\Omega$ of $\\R^2$ with fixed $S^1$-valued boundary condition $g$ of degree $d>0$, the asymptotic behaviour of solutions $u_{\\varepsilon,\\delta}$ of a class of Ginzburg-Landau equations driven by two parameter : the usual Ginzburg-Landau parameter, denoted $\\varepsilon$, and the scale parameter $\\delta$ of a geometry provided by a field of $2\\times 2$ positive definite matrices $x\\to A(\\frac{x}{\\delta})$. The field $\\R^2\\ni x\\to A(x)$ is of class $W^{2,\\infty}$ and periodic. We show, for a suitable choice of the $\\varepsilon$'s depending on $\\delta$, the existence of a limit configuration $u_\\infty\\in H^1_g(\\Omega,S^1)$, which, out of a finite set of singular points, is a weak solution of the equation of $S^1$-valued harmonic functions for the geometry related to the usual homogenized matrix $A^0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-11T23:21:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35J60"
    ],
    "keywords": [
      "periodic unfolding",
      "homogenization",
      "ginzburg-landau equations driven",
      "usual ginzburg-landau parameter",
      "valued harmonic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.1828S"
    }
  }
}