{
  "id": "1404.5162",
  "version": "v1",
  "published": "2014-04-21T10:23:43.000Z",
  "updated": "2014-04-21T10:23:43.000Z",
  "title": "The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems",
  "authors": [
    "Pavel Gurevich"
  ],
  "comment": "39 pages, 5 figures",
  "journal": "Advances in Differential Equations. 11, No. 3 (2006), 305-360",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study smoothness of generalized solutions of nonlocal elliptic problems in plane bounded domains with piecewise smooth boundary. The case where the support of nonlocal terms can intersect the boundary is considered. We find conditions that are necessary and sufficient for any generalized solution to possess an appropriate smoothness (in terms of Sobolev spaces). Both homogeneous and nonhomogeneous nonlocal boundary-value conditions are studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-21T10:23:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35D10",
      "35B65"
    ],
    "keywords": [
      "nonlocal elliptic problems",
      "generalized solution",
      "consistency conditions",
      "nonhomogeneous nonlocal boundary-value conditions",
      "sobolev spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5162G"
    }
  }
}