{
  "id": "2009.08762",
  "version": "v1",
  "published": "2020-09-18T11:59:20.000Z",
  "updated": "2020-09-18T11:59:20.000Z",
  "title": "On the analyticity of solutions to non-linear elliptic partial differential systems",
  "authors": [
    "Simon Blatt"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We give an easy proof of the fact that $C^\\infty$ solutions to non-linear elliptic equations of second order $$ \\phi(x, u, D u, D^2 u)=0 $$ are analytic. Following ideas of Kato, the proof uses an inductive estimate for suitable weighted derivatives. We then conclude the proof using Cauchy's method of majorants}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-18T11:59:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A20",
      "35B65"
    ],
    "keywords": [
      "non-linear elliptic partial differential systems",
      "analyticity",
      "non-linear elliptic equations",
      "second order",
      "cauchys method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}