{
  "id": "2303.02873",
  "version": "v2",
  "published": "2023-03-06T03:52:54.000Z",
  "updated": "2023-05-30T21:06:40.000Z",
  "title": "Harnack Inequalities and Continuity of Solutions under Exponential Logarithmic Orlicz-Sobolev Inequalities",
  "authors": [
    "Lyudmila Korobenko",
    "Cristian Rios",
    "Eric Sawyer",
    "Ruipeng Shen"
  ],
  "comment": "Require major edit on the proof of continuity",
  "categories": [
    "math.AP"
  ],
  "abstract": "In dimensions $n\\geq 2$ we implement the Moser iteration in $\\mathbb{R}^{n}$ endowed with a certain metric $d$ which is topologically equivalent to the Euclidean metric, but for which Lebesgue's measure is not doubling. In this metric space we prove Harnack's inequality for weak solutions to infinitely degenerate quasilinear elliptic equations $-\\mathrm{div}\\mathcal{A}\\left( x,u\\right) \\nabla u=\\phi _{0}-\\mathrm{div}_{A}\\vec{\\phi}_{1}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-05-30T21:06:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inequality",
      "exponential logarithmic orlicz-sobolev inequalities",
      "harnack inequalities",
      "continuity",
      "infinitely degenerate quasilinear elliptic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}