{
  "id": "1912.08983",
  "version": "v1",
  "published": "2019-12-19T01:51:43.000Z",
  "updated": "2019-12-19T01:51:43.000Z",
  "title": "Equivalence between radial solutions of different non-homogeneous $p$-Laplacian type equations",
  "authors": [
    "Jarkko Siltakoski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study radial viscosity solutions to the equation \\[ -\\ |Du\\ |^{q-2}\\Delta_{p}^{N}u=f(\\ |x\\ |)\\quad\\text{in }B_{R}\\subset\\mathbb{R}^{N}, \\] where $f\\in C[0,R)$, $p,q\\in(1,\\infty)$ and $N\\geq2$. Our main result is that $u(x)=v(\\ |x\\ |)$ is a bounded viscosity supersolution if and only if $v$ is a bounded weak supersolution to $-\\kappa\\Delta_{q}^{d}v=f$ in $(0,R)$, where $\\kappa>0$ and $\\Delta_{q}^{d}$ is heuristically speaking the radial $q$-Laplacian in a fictitious dimension $d$. As a corollary we obtain the uniqueness of radial viscosity solutions. However, the full uniqueness of solutions remains an open problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-19T01:51:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35J70",
      "35J75",
      "35D40",
      "35D30"
    ],
    "keywords": [
      "laplacian type equations",
      "radial solutions",
      "equivalence",
      "study radial viscosity solutions",
      "non-homogeneous"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}