{
  "id": "1204.5430",
  "version": "v2",
  "published": "2012-04-24T17:00:45.000Z",
  "updated": "2015-02-05T17:06:06.000Z",
  "title": "On the homotopy Dirichlet problem for p-harmonic maps",
  "authors": [
    "Stefano Pigola",
    "Giona Veronelli"
  ],
  "comment": "26 pages. Corrected typos and references. Changed structure of the paper (but results unchanged)",
  "categories": [
    "math.DG",
    "math.AP"
  ],
  "abstract": "In this two papers we deal with the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to manifolds of non-positive sectional curvature. Notably, we give a complete solution to the problem in case the target manifold is either compact and a new proof in case it is rotationally symmetric or two dimensional and simply connected. The proof of the compact case uses some ideas of White to define the relative d-homotopy type of Sobolev maps, and the regularity theory by Hardt and Lin. To deal with non-compact targets we introduce a periodization procedure which permits to reduce the problem to the previous one. Also, a general uniqueness result is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-24T17:00:45.000Z",
      "abstract": "In this paper we deal with the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to manifolds of non-positive sectional curvature. Notably, we give a complete solution to the problem in case the target manifold is either compact, rotationally symmetric or two dimensional and simply connected. The proof of the compact case uses some ideas of White to define the relative d-homotopy type of Sobolev maps, and the regularity theory by Hardt and Lin. To deal with non-compact targets we introduce a periodization procedure which permits to reduce the problem to the previous one. Also, a general uniqueness result is given.",
      "comment": "30 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-05T17:06:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E20"
    ],
    "keywords": [
      "p-harmonic maps",
      "relative homotopy dirichlet problem",
      "general uniqueness result",
      "non-positive sectional curvature",
      "target manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.5430P"
    }
  }
}