{
  "id": "1411.3668",
  "version": "v1",
  "published": "2014-11-13T19:14:40.000Z",
  "updated": "2014-11-13T19:14:40.000Z",
  "title": "Lipschitz regularity for elliptic equations with random coefficients",
  "authors": [
    "Scott N. Armstrong",
    "Jean-Christophe Mourrat"
  ],
  "comment": "79 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale $L^\\infty$-type estimate for the gradient of a solution. The estimate is proved with optimal stochastic integrability under a one-parameter family of mixing assumptions, allowing for very weak mixing with non-integrable correlations to very strong mixing (e.g., finite range of dependence). We also prove a quenched $L^2$ estimate for the error in homogenization of Dirichlet problems. The approach is based on subadditive arguments which rely on a variational formulation of general quasilinear divergence-form equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-13T19:14:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "60H25",
      "35J20",
      "35J60"
    ],
    "keywords": [
      "random coefficients",
      "lipschitz regularity",
      "general quasilinear divergence-form equations",
      "general quasilinear elliptic equations",
      "optimal stochastic integrability"
    ],
    "publication": {
      "doi": "10.1007/s00205-015-0908-4",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2016,
      "month": "Jan",
      "volume": 219,
      "number": 1,
      "pages": 255
    },
    "note": {
      "typesetting": "TeX",
      "pages": 79,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016ArRMA.219..255A"
    }
  }
}