{
  "id": "1405.2587",
  "version": "v2",
  "published": "2014-05-11T21:24:00.000Z",
  "updated": "2015-10-21T16:15:20.000Z",
  "title": "Potential estimates and quasilinear parabolic equations with measure data",
  "authors": [
    "Quoc Hung Nguyen"
  ],
  "comment": "120 p",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "In this paper, we study the existence and regularity of the quasilinear parabolic equations: $$u_t-\\text{div}(A(x,t,\\nabla u))=B(u,\\nabla u)+\\mu$$ in $\\mathbb{R}^{N+1}$, $\\mathbb{R}^N\\times(0,\\infty)$ and a bounded domain $\\Omega\\times (0,T)\\subset\\mathbb{R}^{N+1}$. Here $N\\geq 2$, the nonlinearity $A$ fulfills standard growth conditions and $B$ term is a continuous function and $\\mu$ is a radon measure. Our first task is to establish the existence results with $B(u,\\nabla u)=\\pm|u|^{q-1}u$, for $q>1$. We next obtain global weighted-Lorentz, Lorentz-Morrey and Capacitary estimates on gradient of solutions with $B\\equiv 0$, under minimal conditions on the boundary of domain and on nonlinearity $A$. Finally, due to these estimates, we solve the existence problems with $B(u,\\nabla u)=|\\nabla u|^q$ for $q>1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-11T21:24:00.000Z",
      "comment": "118 pages. arXiv admin note: text overlap with arXiv:1309.1064 by other authors",
      "journal": null,
      "doi": null,
      "authors": [
        "Nguyen Quoc Hung"
      ]
    },
    {
      "version": "v2",
      "updated": "2015-10-21T16:15:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K58",
      "35K59",
      "31E05",
      "35K67",
      "42B37"
    ],
    "keywords": [
      "quasilinear parabolic equations",
      "measure data",
      "potential estimates",
      "fulfills standard growth conditions",
      "nonlinearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 118,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2587N"
    }
  }
}