{
  "id": "2004.01778",
  "version": "v1",
  "published": "2020-03-22T21:17:51.000Z",
  "updated": "2020-03-22T21:17:51.000Z",
  "title": "Elliptic equations with VMO a, b$\\,\\in L_{d}$, and c$\\,\\in L_{d/2}$",
  "authors": [
    "N. V. Krylov"
  ],
  "comment": "19 p",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We consider elliptic equations with operators $L=a^{ij}D_{ij}+b^{i}D_{i}-c$ with $a$ being almost in VMO, $b\\in L_{d}$ and $c\\in L_{q}$, $c\\geq0$, $d>q\\geq d/2$. We prove the solvability of $Lu=f\\in L_{p}$ in bounded $C^{1,1}$-domains, $1<p\\leq q$, and of $\\lambda u-Lu=f$ in the whole space for any $\\lambda>0$. Weak uniqueness of the martingale problem associated with such operators is also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-22T21:17:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "35J15",
      "60J60"
    ],
    "keywords": [
      "elliptic equations",
      "weak uniqueness",
      "martingale problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}