{
  "id": "2006.03966",
  "version": "v1",
  "published": "2020-06-06T20:36:27.000Z",
  "updated": "2020-06-06T20:36:27.000Z",
  "title": "Recent progress in the $L_p$ theory for elliptic and parabolic equations with discontinuous coefficients",
  "authors": [
    "Hongjie Dong"
  ],
  "comment": "33 pages, submitted",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with VMO$_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$ estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-06T20:36:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parabolic equations",
      "discontinuous coefficients",
      "fully nonlinear elliptic",
      "non-local elliptic",
      "space directions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}