{
  "id": "2111.13795",
  "version": "v2",
  "published": "2021-11-27T02:13:06.000Z",
  "updated": "2022-08-17T20:45:05.000Z",
  "title": "On strong solutions of Itô's equations with $Dσ$ and $b $ in Morrey classes containing $L_{d}$",
  "authors": [
    "N. V. Krylov"
  ],
  "comment": "24 pages. An important example added. arXiv admin note: text overlap with arXiv:2007.06040",
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We consider It\\^o uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W^{1}_{2+\\varepsilon,loc}$, and the drift in a Morrey class containing $L_{d}$. We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-17T20:45:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60J60"
    ],
    "keywords": [
      "morrey classes containing",
      "strong solutions",
      "itôs equations",
      "unique strong solvability",
      "time independent coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}