{
  "id": "2001.01712",
  "version": "v1",
  "published": "2020-01-06T18:55:37.000Z",
  "updated": "2020-01-06T18:55:37.000Z",
  "title": "Remarks on optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form",
  "authors": [
    "Xiaoqin Guo",
    "Hung V. Tran",
    "Yifeng Yu"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study and characterize the optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form. We obtain that the optimal rate of convergence is either $O(\\varepsilon)$ or $O(\\varepsilon^2)$ depending on the diffusion matrix $A$, source term $f$, and boundary data $g$. Moreover, we show that the set of diffusion matrices $A$ that give optimal rate $O(\\varepsilon)$ is open and dense in the set of $C^2$ periodic, symmetric, and positive definite matrices, which means that generically, the optimal rate is $O(\\varepsilon)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-06T18:55:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal rate",
      "linear elliptic equations",
      "periodic homogenization",
      "non-divergence form",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}