{
  "id": "2210.05612",
  "version": "v1",
  "published": "2022-10-11T16:55:41.000Z",
  "updated": "2022-10-11T16:55:41.000Z",
  "title": "Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with Lévy-Noise",
  "authors": [
    "Viorel Barbu",
    "Michael Röckner"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "This work is concerned with the existence of mild solutions to non-linear Fokker-Planck equations with fractional Laplace operator $(-\\Delta)^s$ for $s\\in\\left(\\frac12,1\\right)$. The uniqueness of Schwartz distributional solutions is also proved under suitable assumptions on diffusion and drift terms. As applications, weak existence and uniqueness of solutions to McKean-Vlasov equations with L\\'evy-Noise, as well as the Markov property for their laws are proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-11T16:55:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "47H05",
      "47J05"
    ],
    "keywords": [
      "nonlinear fokker-planck equations",
      "fractional laplacian",
      "mckean-vlasov sdes",
      "lévy-noise",
      "schwartz distributional solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}