{
  "id": "1403.5192",
  "version": "v1",
  "published": "2014-03-20T16:31:29.000Z",
  "updated": "2014-03-20T16:31:29.000Z",
  "title": "Traces for functions of bounded variation on manifolds with applications to conservation laws on manifolds with boundary",
  "authors": [
    "Dietmar Kröner",
    "Thomas Müller",
    "Lena Maria Strehlau"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we show existence of a trace for functions of bounded variation on Riemannian manifolds with boundary. The trace, which is bounded in $L^\\infty$, is reached via $L^1$-convergence and allows an integration by parts formula. We apply these results in order to show well-posedness and total variation estimates for the initial boundary value problem for a scalar conservation law on compact Riemannian manifolds with boundary in the context of functions of bounded variation via the vanishing viscosity method. The flux function is assumed to be time-dependent and divergence-free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-20T16:31:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "58J45",
      "76N10"
    ],
    "keywords": [
      "bounded variation",
      "applications",
      "initial boundary value problem",
      "total variation estimates",
      "scalar conservation law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.5192K"
    }
  }
}