{
  "id": "2103.05177",
  "version": "v1",
  "published": "2021-03-09T02:11:08.000Z",
  "updated": "2021-03-09T02:11:08.000Z",
  "title": "$q$-Moment Estimates for the Singular $p$-Laplace Equation and Applications",
  "authors": [
    "Samuel Drapeau",
    "Liming Yin"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We provide $q$-moment estimates on annuli for weak solutions of the singular $p$-Laplace equation where $p$ and $q$ are conjugates. We derive $q$-uniform integrability for some critical parameter range. As a application, we derive a mass conservation as well as a weak convergence result for a larger critical parameter range. Concerning the latter point, we further provide a rate of convergence of order $t^{q-1}$ of the solution in the $q$-Wasserstein distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-09T02:11:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K92",
      "35B45",
      "35Q49"
    ],
    "keywords": [
      "laplace equation",
      "moment estimates",
      "application",
      "larger critical parameter range",
      "weak convergence result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}