{
  "id": "1412.5850",
  "version": "v1",
  "published": "2014-12-18T13:22:06.000Z",
  "updated": "2014-12-18T13:22:06.000Z",
  "title": "Concentrated terms and varying domains in elliptic equations: Lipschitz case",
  "authors": [
    "G. S. Aragão",
    "S. M Bruschi"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we analyze the behavior of a family of solutions of a nonlinear elliptic equation with nonlinear boundary conditions, when the boundary of the domain presents a highly oscillatory behavior which is uniformly Lipschitz and nonlinear terms are concentrated in a region which neighbors the boundary domain. We prove that this family of solutions converges to the solutions of a limit problem in H^1 , an elliptic equation with nonlinear boundary conditions which captures the oscillatory behavior of the boundary and whose nonlinear terms are transformed into a flux condition on the boundary. Indeed, we show the upper semicontinuity of this family of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-18T13:22:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "34B15"
    ],
    "keywords": [
      "lipschitz case",
      "varying domains",
      "concentrated terms",
      "nonlinear boundary conditions",
      "oscillatory behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}