{
  "id": "1912.00724",
  "version": "v1",
  "published": "2019-12-02T12:48:43.000Z",
  "updated": "2019-12-02T12:48:43.000Z",
  "title": "Quantitative homogenization for the case of an interface between two heterogeneous media",
  "authors": [
    "Marc Josien",
    "Claudia Raithel"
  ],
  "comment": "58 pages, 5 Figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we are interested in quantitative homogenization results for linear elliptic equations in the non-stationary situation of a straight interface between two heterogenous media. This extends the previous work [Josien, 2019] to a substantially more general setting, in which the surrounding heterogeneous media may be periodic or random stationary and ergodic. Our main result is a quantification of the sublinearity of a homogenization corrector adapted to the interface, which we construct using an improved version of the method developed in [Fischer and Raithel, 2017]. This quantification is optimal up to a logarithmic loss and allows to derive almost-optimal convergence rates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-02T12:48:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "35B40",
      "35J15",
      "35J25"
    ],
    "keywords": [
      "heterogeneous media",
      "linear elliptic equations",
      "derive almost-optimal convergence rates",
      "non-stationary situation",
      "quantitative homogenization results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}