{
  "id": "1611.02125",
  "version": "v1",
  "published": "2016-11-07T15:46:52.000Z",
  "updated": "2016-11-07T15:46:52.000Z",
  "title": "Existence of solutions to degenerate parabolic problems with two weights via the Hardy inequality",
  "authors": [
    "Iwona Skrzypczak",
    "Anna Zatorska-Goldstein"
  ],
  "comment": "18 pages, submitted",
  "categories": [
    "math.AP"
  ],
  "abstract": "The paper concentrates on the application of the following Hardy inequality \\begin{equation*} \\int_\\Omega \\ |\\xi(x)|^p \\omega_{1 }(x)dx\\le \\int_\\Omega |\\nabla \\xi(x)|^p\\omega_{2 }(x)dx, \\end{equation*} to the proof of existence of weak solutions to degenerate parabolic problems of the type \\begin{equation*} \\left\\{\\begin{array}{ll} u_t-div(\\omega_2(x)|\\nabla u|^{p-2} \\nabla u )= \\lambda W(x) |u|^{p-2}u& x\\in\\Omega, u(x,0)=f(x)& x\\in\\Omega, u(x,t)=0& x\\in\\partial\\Omega,\\ t>0,\\\\ \\end{array}\\right. \\end{equation*} on an open subset $\\Omega\\subseteq\\mathbb{R}^n$, not necessarily bounded, where \\[W(x)\\leq \\min\\{m,\\omega_1(x)\\},\\qquad m\\in\\mathbb{R}_+.\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-07T15:46:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35A01",
      "47J35"
    ],
    "keywords": [
      "degenerate parabolic problems",
      "hardy inequality",
      "paper concentrates",
      "weak solutions",
      "open subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}