{
  "id": "1505.02330",
  "version": "v1",
  "published": "2015-05-10T00:13:15.000Z",
  "updated": "2015-05-10T00:13:15.000Z",
  "title": "On parabolic equations in one space dimension",
  "authors": [
    "N. V. Krylov"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of $(t,x)$ bounded away from zero. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-10T00:13:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "35K15"
    ],
    "keywords": [
      "space dimension",
      "inhomogeneous second-order uniformly parabolic equations",
      "lower order terms",
      "cauchy problem",
      "fundamental solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150502330K"
    }
  }
}