{
  "id": "1905.00168",
  "version": "v1",
  "published": "2019-05-01T03:00:26.000Z",
  "updated": "2019-05-01T03:00:26.000Z",
  "title": "On viscosity solutions of space-fractional diffusion equations of Caputo type",
  "authors": [
    "Tokinaga Namba",
    "Piotr Rybka"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary values by Perron's method. Their uniqueness follows from a proper maximum principle. We also show a stability result and basic regularity of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-01T03:00:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solution",
      "space-fractional diffusion equations",
      "caputo type",
      "fractional diffusion problem",
      "dirichlet boundary values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}