{
  "id": "2008.04366",
  "version": "v1",
  "published": "2020-08-10T18:59:44.000Z",
  "updated": "2020-08-10T18:59:44.000Z",
  "title": "Large-Scale Lipschitz Estimates for Elliptic Systems with Periodic High-Contrast Coefficients",
  "authors": [
    "Zhongwei Shen"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with the large-scale regularity in the homogenization of elliptic systems of elasticity with periodic high-contrast coefficients. We obtain the large-scale Lipschitz estimate that is uniform with respect to the contrast ratio $\\delta^2$ for $0<\\delta<\\infty$. Our study also covers the case of soft inclusions ($\\delta=0$) as well as the case of stiff inclusions ($\\delta=\\infty$). The large-scale Lipschitz estimate, together with classical local estimates, allows us to establish explicit bounds for the matrix of fundamental solutions and its derivatives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-10T18:59:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "74Q05"
    ],
    "keywords": [
      "large-scale lipschitz estimate",
      "periodic high-contrast coefficients",
      "elliptic systems",
      "establish explicit bounds",
      "contrast ratio"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}