{
  "id": "2403.18738",
  "version": "v1",
  "published": "2024-03-27T16:27:23.000Z",
  "updated": "2024-03-27T16:27:23.000Z",
  "title": "The extension of traces for Sobolev mappings between manifolds",
  "authors": [
    "Jean Van Schaftingen"
  ],
  "comment": "56 pages",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "The compact Riemannian manifolds $\\mathcal{M}$ and $\\mathcal{N}$ for which the trace operator from the first-order Sobolev space of mappings $\\smash{\\dot{W}}^{1, p} (\\mathcal{M}, \\mathcal{N})$ to the fractional Sobolev-Slobodecki\\u{\\i} space $\\smash{\\smash{\\dot{W}}^{1 - 1/p, p}} (\\partial \\mathcal{M}, \\mathcal{N})$ is surjective when $1 < p < m$ are characterised. The traces are extended using a new construction which can be carried out assuming the absence of the known topological and analytical obstructions. When $p \\ge m$ the same construction provides a Sobolev extension with linear estimates for maps that have a continuous extension, provided that there are no known analytical obstructions to such a control.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-27T16:27:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58D15",
      "46E35",
      "46T10",
      "58C25",
      "58J32"
    ],
    "keywords": [
      "sobolev mappings",
      "first-order sobolev space",
      "compact riemannian manifolds",
      "analytical obstructions",
      "construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}