{
  "id": "1409.5575",
  "version": "v1",
  "published": "2014-09-19T09:59:55.000Z",
  "updated": "2014-09-19T09:59:55.000Z",
  "title": "Renormalized solutions of nonlinear parabolic equations with general measure data",
  "authors": [
    "Francesco Petitta"
  ],
  "journal": "Ann. Mat. Pura ed Appl., 187 (4) (2008), 563-604",
  "doi": "10.1007/s10231-007-0057-y",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $\\Omega\\subseteq \\mathbb{R}^N$ a bounded open set, $N\\geq 2$, and let $p>1$; we prove existence of a renormalized solution for parabolic problems whose model is $$ \\begin{cases} u_{t}-\\Delta_{p} u=\\mu & \\text{in}\\ (0,T)\\times\\Omega,\\newline u(0,x)=u_0 & \\text{in}\\ \\Omega,\\newline u(t,x)=0 &\\text{on}\\ (0,T)\\times\\partial\\Omega, \\end{cases} $$ where $T>0$ is any positive constant, $\\mu\\in M(Q)$ is a any measure with bounded variation over $Q=(0,T)\\times\\Omega$, and $u_o\\in L^1(\\Omega)$, and $-\\Delta_{p} u=-{\\rm div} (|\\nabla u|^{p-2}\\nabla u )$ is the usual $p$-laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-19T09:59:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general measure data",
      "nonlinear parabolic equations",
      "renormalized solution",
      "bounded open set",
      "parabolic problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.5575P"
    }
  }
}