{
  "id": "1712.01196",
  "version": "v1",
  "published": "2017-12-04T17:02:48.000Z",
  "updated": "2017-12-04T17:02:48.000Z",
  "title": "Fractional-order operators: Boundary problems, heat equations",
  "authors": [
    "Gerd Grubb"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\\\"older estimates in the time-parameter) based on a general result of Amann.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-04T17:02:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K05",
      "35K25",
      "47G30",
      "60G52"
    ],
    "keywords": [
      "fractional-order operators",
      "boundary problems",
      "nonhomogeneous local boundary conditions",
      "higher regularity estimates",
      "homogeneous dirichlet condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}