{
  "id": "1207.2263",
  "version": "v2",
  "published": "2012-07-10T08:32:37.000Z",
  "updated": "2013-06-23T12:09:16.000Z",
  "title": "Dirichlet forms and semilinear elliptic equations with measure data",
  "authors": [
    "Tomasz Klimsiak",
    "Andrzej Rozkosz"
  ],
  "comment": "Typos corrected. Two examples added",
  "journal": "J. Funct. Anal. 265 (2013) 890-925",
  "doi": "10.1016/j.jfa.2013.05.028",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal) operators associated with regular Dirichlet forms and with measure data. Using the theory of backward stochastic differential equations we prove the existence and uniqueness of solutions in the case where the right-hand side of the equation is monotone and satisfies mild integrability assumption, and the measure is smooth. We also study regularity of solutions under the assumption that the measure is smooth and has finite total variation. Some applications of our general results are given.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-23T12:09:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35R06",
      "60H30"
    ],
    "keywords": [
      "semilinear elliptic equations",
      "measure data",
      "satisfies mild integrability assumption",
      "regular dirichlet forms",
      "backward stochastic differential equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.2263K"
    }
  }
}