{
  "id": "2011.00933",
  "version": "v1",
  "published": "2020-11-02T12:29:54.000Z",
  "updated": "2020-11-02T12:29:54.000Z",
  "title": "A new proof of the Gaffney's inequality for differential forms on manifolds-with-boundary: the variational approach à la Kozono--Yanagisawa",
  "authors": [
    "Siran Li"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AP",
    "math.DG",
    "math.HO"
  ],
  "abstract": "Let $(\\mathcal{M},g_0)$ be a compact Riemannian manifold-with-boundary. We present a new proof of the classical Gaffney's inequality for differential forms in boundary value spaces over $\\mathcal{M}$, via the variational approach \\`{a} la Kozono--Yanagisawa [$L^r$-variational inequality for vector fields and the Helmholtz--Weyl decomposition in bounded domains, Indiana Univ. Math. J. 58 (2009), 1853--1920] combined with global computations based on the Bochner's technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-02T12:29:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58A10",
      "58J32"
    ],
    "keywords": [
      "differential forms",
      "variational approach",
      "kozono-yanagisawa",
      "manifolds-with-boundary",
      "boundary value spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}