{
  "id": "1503.05039",
  "version": "v1",
  "published": "2015-03-17T13:34:46.000Z",
  "updated": "2015-03-17T13:34:46.000Z",
  "title": "Elliptic boundary-value problems in the sense of Lawruk on Sobolev and Hörmander spaces",
  "authors": [
    "Iryna S. Chepurukhina",
    "Aleksandr A. Murach"
  ],
  "comment": "22 pages. arXiv admin note: substantial text overlap with arXiv:1412.0495",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate elliptic boundary-value problems with additional unknown functions in boundary conditions. These problems were introduced by Lawruk. We prove that the operator corresponding to such a problem is bounded and Fredholm on appropriate couples of the inner product isotropic H\\\"ormander spaces $H^{s,\\varphi}$, which form the refined Sobolev scale. The order of differentiation for these spaces is given by the real number $s$ and positive function $\\varphi$ that varies slowly at infinity in the sense of Karamata. We consider this problem for an arbitrary elliptic equation $Au=f$ on a bounded Euclidean domain $\\Omega$ under the condition that $u\\in H^{s,\\varphi}(\\Omega)$, $s<\\mathrm{ord}\\,A$, and $f\\in L_{2}(\\Omega)$. We prove theorems on the a priori estimate and regularity of the generalized solutions to this problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-17T13:34:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J40",
      "46E35"
    ],
    "keywords": [
      "elliptic boundary-value problems",
      "hörmander spaces",
      "additional unknown functions",
      "inner product isotropic",
      "arbitrary elliptic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}