{
  "id": "2001.05435",
  "version": "v1",
  "published": "2020-01-15T17:12:20.000Z",
  "updated": "2020-01-15T17:12:20.000Z",
  "title": "Linear and fully nonlinear elliptic equations with $L_{d}$-drift",
  "authors": [
    "N. V. Krylov"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In subdomains of $\\mathbb{R}^{d}$ we consider uniformly elliptic equations $H\\big(v( x),D v( x),D^{2}v( x), x\\big)=0$ with the growth of $H$ with respect to $|Dv|$ controlled by the product of a function from $L_{d}$ times $|Dv|$. The dependence of $H$ on $x$ is assumed to be of BMO type. Among other things we prove that there exists $d_{0}\\in(d/2,d)$ such that for any $p\\in(d_{0},d)$ the equation with prescribed continuous boundary data has a solution in class $W^{2}_{p,\\text{loc}}$. Our results are new even if $H$ is linear.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-15T17:12:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J15"
    ],
    "keywords": [
      "fully nonlinear elliptic equations",
      "bmo type",
      "uniformly elliptic equations",
      "prescribed continuous boundary data",
      "subdomains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}