{
  "id": "2203.14181",
  "version": "v1",
  "published": "2022-03-27T01:19:33.000Z",
  "updated": "2022-03-27T01:19:33.000Z",
  "title": "On a sharp inequality of Adimurthi-Druet type and extremal functions",
  "authors": [
    "José Francisco de Oliveira",
    "João Marcos do Ó"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Our main purpose in this paper is to establish the existence and nonexistence of extremal functions for sharp inequality of Adimurthi-Druet type for fractional dimensions on the entire space. Precisely, we extend the sharp Trudinger-Moser type inequality in (Calc.Var.Partial Differential Equations, \\textbf{52} (2015) 125-163) for the entire space. In addition, we perform the two-step strategy of Carleson-Chang together blow up analysis method to ensure the existence of maximizers for the associated extremal problems for both subcritical and critical regimes. We also present a nonexistence result under subcritical regime for some special cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-27T01:19:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "46E35",
      "26D10",
      "35B33"
    ],
    "keywords": [
      "extremal functions",
      "adimurthi-druet type",
      "sharp inequality",
      "sharp trudinger-moser type inequality",
      "entire space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}