{
  "id": "2006.08984",
  "version": "v1",
  "published": "2020-06-16T08:29:50.000Z",
  "updated": "2020-06-16T08:29:50.000Z",
  "title": "On initial boundary value problem for parabolic differential operator with non-coercive boundary conditions",
  "authors": [
    "Alexander Polkovnikov"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in ${\\mathbb R}^n $ with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-16T08:29:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial boundary value problem",
      "non-coercive boundary conditions",
      "parabolic differential operator",
      "special bochner space",
      "sobolev type spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}