{
  "id": "1805.05136",
  "version": "v1",
  "published": "2018-05-14T12:13:28.000Z",
  "updated": "2018-05-14T12:13:28.000Z",
  "title": "Regularizing effect for some p-Laplacian systems",
  "authors": [
    "Riccardo Durastanti"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study existence and regularity of weak solutions for the following $p$-Laplacian system \\begin{cases} -\\Delta_p u+A\\varphi^{\\theta+1}|u|^{r-2}u=f, \\ &u\\in W_0^{1,p}(\\Omega),\\\\-\\Delta_p \\varphi=|u|^r\\varphi^\\theta, \\ &\\varphi\\in W_0^{1,p}(\\Omega), \\end{cases} where $\\Omega$ is an open bounded subset of $\\mathbb{R}^N$ $(N\\geq 2)$, $\\Delta_p v :=\\operatorname{div}(|\\nabla v|^{p-2}\\nabla v)$ is the $p$-Laplacian operator, for $1<p<N$, $A>0$, $r>1$, $0\\leq\\theta<p-1$ and $f$ belongs to a suitable Lebesgue space. In particular, we show how the coupling between the equations in the system gives rise to a regularizing effect producing the existence of finite energy solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-14T12:13:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regularizing effect",
      "p-laplacian systems",
      "finite energy solutions",
      "weak solutions",
      "suitable lebesgue space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}