{
  "id": "2211.13180",
  "version": "v1",
  "published": "2022-11-23T17:56:23.000Z",
  "updated": "2022-11-23T17:56:23.000Z",
  "title": "Logarithmic Sobolev and interpolation inequalities on the sphere: constructive stability results",
  "authors": [
    "Giovanni Brigati",
    "Jean Dolbeault",
    "Nikita Simonov"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincar\\'e inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability results in the subcritical regime using spectral decomposition techniques, and entropy and carr\\'e du champ methods applied to nonlinear diffusion flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-23T17:56:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "58J99",
      "39B62",
      "43A90",
      "49J40",
      "46E35"
    ],
    "keywords": [
      "constructive stability results",
      "interpolation inequalities",
      "nonlinear diffusion flows",
      "logarithmic sobolev inequality",
      "spectral decomposition techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}