{
  "id": "1306.5340",
  "version": "v4",
  "published": "2013-06-22T17:53:37.000Z",
  "updated": "2019-11-30T23:25:37.000Z",
  "title": "Quantitative stochastic homogenization of elliptic equations in nondivergence form",
  "authors": [
    "Scott N. Armstrong",
    "Charles K. Smart"
  ],
  "comment": "40 pages. This version correctors some minor mistakes in the published version of the article. The changes are described in Section 1.5",
  "journal": "Arch. Ration. Mech. Anal., 214 (2014), 867-911",
  "doi": "10.1007/s00205-014-0765-6",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional to a power of the microscopic length scale, assuming a finite range of dependence. The results are new even for linear equations. The arguments rely on a new geometric quantity which is controlled in part by adapting elements of the regularity theory for the Monge-Amp\\`ere equation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-04T15:33:22.000Z",
      "comment": "39 pages. Minor revision",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2019-11-30T23:25:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "35J60",
      "60F17"
    ],
    "keywords": [
      "quantitative stochastic homogenization",
      "elliptic equations",
      "nondivergence form",
      "algebraic error estimate",
      "microscopic length scale"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-014-0765-6",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2014,
      "month": "Jun",
      "pages": 59,
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014ArRMA.tmp...59A"
    }
  }
}