{
  "id": "1603.03139",
  "version": "v1",
  "published": "2016-03-10T03:52:47.000Z",
  "updated": "2016-03-10T03:52:47.000Z",
  "title": "Approximate Correctors and Convergence Rates in Almost-Periodic Homogenization",
  "authors": [
    "Zhongwei Shen",
    "Jinping Zhuge"
  ],
  "comment": "48 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with quantitative homogenization of second-order elliptic systems with bounded measurable coefficients that are almost-periodic in the sense of H. Weyl. We obtain uniform local $L^2$ estimates for the approximate correctors in terms of a function that quantifies the almost-periodicity of the coefficient matrix. We give a condition that implies the existence of (true) correctors. These estimates as well as similar estimates for the dual approximate correctors yield optimal or near optimal convergence rates in $H^1$ and $L^2$. The $L^2$-based H\\\"older and Lipschitz estimates at large scale are also established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-10T03:52:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "74Q20"
    ],
    "keywords": [
      "almost-periodic homogenization",
      "dual approximate correctors yield optimal",
      "second-order elliptic systems",
      "optimal convergence rates",
      "coefficient matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160303139S"
    }
  }
}