{
  "id": "1408.2469",
  "version": "v2",
  "published": "2014-08-11T17:02:06.000Z",
  "updated": "2015-09-09T00:11:56.000Z",
  "title": "Solvability and regularity for an elliptic system prescribing the curl, divergence, and partial trace of a vector field on Sobolev-class domains",
  "authors": [
    "C. H. Arthur Cheng",
    "Steve Shkoller"
  ],
  "comment": "49 Pages, improved exposition and corrected typos",
  "categories": [
    "math.AP"
  ],
  "abstract": "We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field are prescribed in an open, bounded, Sobolev-class domain, and either the normal component or the tangential components of the vector field are prescribed on the boundary. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-11T17:02:06.000Z",
      "abstract": "We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field are prescribed in an open, bounded, Sobolev-class domain, and either the normal component or the tangential components of the vector field are prescribed on the boundary.",
      "comment": "42 Pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-09-09T00:11:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J57",
      "58A14"
    ],
    "keywords": [
      "vector field",
      "elliptic system prescribing",
      "sobolev-class domain",
      "partial trace",
      "divergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.2469C"
    }
  }
}