{
  "id": "1508.05519",
  "version": "v1",
  "published": "2015-08-22T15:01:15.000Z",
  "updated": "2015-08-22T15:01:15.000Z",
  "title": "Mollification of $\\mathcal{D}$-solutions to Fully Nonlinear PDE Systems",
  "authors": [
    "Nikos Katzourakis"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In a recent paper (arXiv:1501.06164) the author has introduced a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows the interpretation of merely measurable maps as solutions. This approach is duality-free and builds on the probabilistic representation of limits of difference quotients via Young measures over certain compactifications of the \"state space\". Herein we establish a systematic regularisation scheme of this notion of solution which, by analogy, is the counterpart of the usual mollification by convolution of weak solutions and of the mollification by sup/inf convolutions of viscosity solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-22T15:01:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fully nonlinear pde systems",
      "systematic regularisation scheme",
      "usual mollification",
      "viscosity solutions",
      "sup/inf convolutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}