{
  "id": "2111.09603",
  "version": "v1",
  "published": "2021-11-18T10:08:24.000Z",
  "updated": "2021-11-18T10:08:24.000Z",
  "title": "A comparison principle for the Lane-Emden equation and applications to geometric estimates",
  "authors": [
    "Lorenzo Brasco",
    "Francesca Prinari",
    "Anna Chiara Zagati"
  ],
  "comment": "42 pages",
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "We prove a comparison principle for positive supersolutions and subsolutions to the Lane-Emden equation for the $p-$Laplacian, with subhomogeneous power in the right-hand side. The proof uses variational tools and the result applies with no regularity assumptions, both on the set and the functions. We then show that such a comparison principle can be applied to prove: uniqueness of solutions; sharp pointwise estimates for positive solutions in convex sets; localization estimates for maximum points and sharp geometric estimates for generalized principal frequencies in convex sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-11-18T10:08:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B51",
      "35J92",
      "49R05"
    ],
    "keywords": [
      "comparison principle",
      "lane-emden equation",
      "applications",
      "convex sets",
      "sharp geometric estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}