{
  "id": "2502.00825",
  "version": "v1",
  "published": "2025-02-02T15:43:10.000Z",
  "updated": "2025-02-02T15:43:10.000Z",
  "title": "An overview of regularity results for the Laplacian and $p$-Laplacian in metric spaces",
  "authors": [
    "Ivan Yuri Violo"
  ],
  "categories": [
    "math.AP",
    "math.MG"
  ],
  "abstract": "We review some regularity results for the Laplacian and $p$-Laplacian in metric measure spaces. The focus is mainly on interior H\\\"older, Lipschitz and second-regularity estimates and on spaces supporting a Poincar\\'e inequality or having Ricci curvature bounded below.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-02T15:43:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J92",
      "46E36",
      "58J05"
    ],
    "keywords": [
      "regularity results",
      "metric spaces",
      "metric measure spaces",
      "poincare inequality",
      "ricci curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}