{
  "id": "1412.0495",
  "version": "v1",
  "published": "2014-12-01T14:48:17.000Z",
  "updated": "2014-12-01T14:48:17.000Z",
  "title": "Elliptic problems in the sense of B. Lawruk on two-sided refined scales of spaces",
  "authors": [
    "Iryna S. Chepurukhina",
    "Aleksandr A. Murach"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate elliptic boundary-value problems with additional unknown functions on the boundary of a Euclidean domain. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and Fredholm on two-sided refined scales built on the base of inner product isotropic H\\\"ormander spaces. The regularity of the distributions forming these spaces are characterized by a real number and an arbitrary function that varies slowly at infinity in the sense of Karamata. For the generalized solutions to the problem, we prove theorems on a priori estimates and local regularity in these scales. As applications, we find new sufficient conditions under which the solutions have continuous classical derivatives of a prescribed order.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-01T14:48:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J40",
      "46E35"
    ],
    "keywords": [
      "two-sided refined scales",
      "elliptic problems",
      "elliptic boundary-value problems",
      "additional unknown functions",
      "inner product isotropic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.0495C"
    }
  }
}