{
  "id": "2102.12414",
  "version": "v1",
  "published": "2021-02-24T17:07:31.000Z",
  "updated": "2021-02-24T17:07:31.000Z",
  "title": "Renormalized solutions for stochastic $p$-Laplace equation with $L^1$-initial data: The multiplicative case",
  "authors": [
    "Niklas Sapountzoglou",
    "Aleksandra Zimmermann"
  ],
  "comment": "27 pages. arXiv admin note: substantial text overlap with arXiv:1908.11186",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We consider a $p$-Laplace evolution problem with multiplicative noise on a bounded domain $D \\subset \\mathbb{R}^d$ with homogeneous Dirichlet boundary conditions for $1<p< \\infty$. The random initial data is merely integrable. Consequently, the key estimates are available with respect to truncations of the solution. We introduce the notion of renormalized solutions for multiplicative stochastic $p$-Laplace equation with $L^1$ initial data and study existence and uniqueness of solutions in this framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-24T17:07:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35R60",
      "60H15",
      "35D99"
    ],
    "keywords": [
      "laplace equation",
      "renormalized solutions",
      "multiplicative case",
      "stochastic",
      "laplace evolution problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}