{
  "id": "1201.4573",
  "version": "v1",
  "published": "2012-01-22T16:57:23.000Z",
  "updated": "2012-01-22T16:57:23.000Z",
  "title": "Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients",
  "authors": [
    "N. V. Krylov"
  ],
  "comment": "23 pages, submitted",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order equations in \\cite{DKL}. The first type is an estimate of the $\\gamma$th norm of the second-order derivatives, where $\\gamma\\in(0,1)$, and the second type deals with estimates of the resolvent operators in $L_{p}$ when the first-order coefficients are summable to an appropriate power.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-22T16:57:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J15",
      "35K10",
      "60H10"
    ],
    "keywords": [
      "measurable coefficients",
      "parabolic operators",
      "parabolic second order equations",
      "second type deals",
      "parabolic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.4573K"
    }
  }
}