{
  "id": "2005.12776",
  "version": "v1",
  "published": "2020-05-26T14:55:46.000Z",
  "updated": "2020-05-26T14:55:46.000Z",
  "title": "Combined Effects of Homogenization and Singular Perturbations: Quantitative Estimates",
  "authors": [
    "Weisheng Niu",
    "Zhongwei Shen"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale $\\kappa$ that represents the strength of the singular perturbation and on the length scale $\\epsilon$ of the heterogeneities, are established. We also obtain the large-scale Lipschitz estimate, down to the scale $\\epsilon$ and independent of $\\kappa$. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both $\\epsilon$ and $\\kappa$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T14:55:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "35B25"
    ],
    "keywords": [
      "singular perturbation",
      "quantitative estimates",
      "second-order elliptic systems",
      "large-scale lipschitz estimate",
      "singular fourth-order perturbations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}