{
  "id": "1806.05428",
  "version": "v1",
  "published": "2018-06-14T09:23:53.000Z",
  "updated": "2018-06-14T09:23:53.000Z",
  "title": "Global L^r-estimates and regularizing effect for solutions to the p(t, x) -Laplacian systems",
  "authors": [
    "Francesca Crispo",
    "Paolo Maremonti",
    "Michael Ruzicka"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the initial boundary value problem for the p(t, x)-Laplacian system in a bounded domain \\Omega. If the initial data belongs to L^{r_0}, r_0 \\geq 2, we give a global L^{r_0}({\\Omega})-regularity result uniformly in t>0 that, in the particular case r_0 =\\infty, implies a maximum modulus theorem. Under the assumption p- = \\inf p(t, x) > 2n/(n+r_0), we also state L^{r_0}- L^r estimates for the solution, for r \\geq r_0. Complete proofs of the results presented here are given in the paper [F. Crispo, P. Maremonti, M. Ruzicka, Global L^r-estimates and regularizing effect for solutions to the p(t, x) -Laplacian systems, accepted for publication on Advances in Differential Equations, 2017].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-14T09:23:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "laplacian systems",
      "regularizing effect",
      "initial boundary value problem",
      "maximum modulus theorem",
      "initial data belongs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}