{
  "id": "1105.4511",
  "version": "v1",
  "published": "2011-05-23T14:22:02.000Z",
  "updated": "2011-05-23T14:22:02.000Z",
  "title": "From Poincaré to logarithmic Sobolev inequalities: a gradient flow approach",
  "authors": [
    "Jean Dolbeault",
    "Bruno Nazaret",
    "Giuseppe Savaré"
  ],
  "journal": "SIAM J. Math. Anal. 44, 5 (2012) 3186-3216",
  "categories": [
    "math.AP"
  ],
  "abstract": "We use the distances introduced in a previous joint paper to exhibit the gradient flow structure of some drift-diffusion equations for a wide class of entropy functionals. Functional inequalities obtained by the comparison of the entropy with the entropy production functional reflect the contraction properties of the flow. Our approach provides a unified framework for the study of the Kolmogorov-Fokker-Planck (KFP) equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-23T14:22:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient flow approach",
      "logarithmic sobolev inequalities",
      "entropy production functional reflect",
      "gradient flow structure",
      "drift-diffusion equations"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1105.4511D"
    }
  }
}