{
  "id": "1507.06518",
  "version": "v1",
  "published": "2015-07-23T14:49:27.000Z",
  "updated": "2015-07-23T14:49:27.000Z",
  "title": "Renormalized solutions of semilinear equations involving measure data and operator corresponding to Dirichlet form",
  "authors": [
    "Tomasz Klimsiak",
    "Andrzej Rozkosz"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We generalize the notion of renormalized solution to semilinear elliptic and parabolic equations involving operator associated with general (possibly nonlocal) regular Dirichlet form and smooth measure on the right-hand side. We show that under mild integrability assumption on the data a quasi-continuous function $u$ is a renormalized solution to an elliptic (or parabolic) equation in the sense of our definition iff $u$ is its probabilistic solution, i.e. $u$ can be represented by a suitable nonlinear Feynman-Kac formula. This implies in particular that for a broad class of local and nonlocal semilinear equations there exists a unique renormalized solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-23T14:49:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35D99",
      "35J61",
      "35K58",
      "60H30"
    ],
    "keywords": [
      "measure data",
      "operator corresponding",
      "regular dirichlet form",
      "suitable nonlinear feynman-kac formula",
      "mild integrability assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}