{
  "id": "1702.03746",
  "version": "v1",
  "published": "2017-02-13T12:46:50.000Z",
  "updated": "2017-02-13T12:46:50.000Z",
  "title": "Nonlinear diffusion in transparent media: the resolvent equation",
  "authors": [
    "Lorenzo Giacomelli",
    "Salvador Moll",
    "Francesco Petitta"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the partial differential equation $$ u-f={\\rm div}\\left(u^m\\frac{\\nabla u}{|\\nabla u|}\\right) $$ with $f$ nonnegative and bounded and $m\\in\\mathbb{R}$. We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative {boundary datum}) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the ${\\mathcal H}^{N-1}$ Haussdorff measure. Results and proofs extend to more general nonlinearities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-13T12:46:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35J60",
      "35B51",
      "35B99"
    ],
    "keywords": [
      "resolvent equation",
      "transparent media",
      "nonlinear diffusion",
      "partial differential equation",
      "zero jump part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}