{
  "id": "0904.0372",
  "version": "v1",
  "published": "2009-04-02T12:09:06.000Z",
  "updated": "2009-04-02T12:09:06.000Z",
  "title": "Elliptic problems and Hörmander spaces",
  "authors": [
    "Vladimir A. Mikhailets",
    "Aleksandr A. Murach"
  ],
  "comment": "20 papges",
  "journal": "Operator Theory: Advances and Applications, vol. 191, Birkh\\\"auser-Verlag, Basel, 2009, pp. 447--470.",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "The paper gives a survey of the modern results on elliptic problems on the H\\\"ormander function spaces. More precisely, elliptic problems are studied on a Hilbert scale of the isotropic H\\\"ormander spaces parametrized by a real number and a function slowly varying at $+\\infty$ in the Karamata sense. This refined scale is finer than the Sobolev scale and is closed with respect to the interpolation with a function parameter. The Fredholm property of elliptic operators and elliptic boundary-value problems is preserved for this scale. A local refined smoothness of the elliptic problem solution is studied. An abstract construction of classes of function spaces in which the elliptic problem is a Fredholm one is found. In particular, some generalizations of the Lions-Magenes theorems are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-02T12:09:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J30",
      "35J40",
      "46E35"
    ],
    "keywords": [
      "hörmander spaces",
      "function spaces",
      "elliptic boundary-value problems",
      "elliptic problem solution",
      "hilbert scale"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0372M"
    }
  }
}