{
  "id": "1601.04492",
  "version": "v1",
  "published": "2016-01-18T12:42:29.000Z",
  "updated": "2016-01-18T12:42:29.000Z",
  "title": "Superposition in the $p$-Laplace Equation",
  "authors": [
    "Karl K. Brustad"
  ],
  "comment": "14 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "That a superposition of fundamental solutions to the $p$-Laplace Equation is $p$-superharmonic -- even in the non-linear cases $p>2$ -- has been known since M. Crandall and J. Zhang published their paper \"Another Way to Say Harmonic\" in 2003. We give a simple proof and extend the result by means of an explicit formula for the $p$-Laplacian of the superposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-18T12:42:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "laplace equation",
      "superposition",
      "fundamental solutions",
      "non-linear cases",
      "simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160104492B"
    }
  }
}