{
  "id": "1810.04818",
  "version": "v1",
  "published": "2018-10-11T02:02:04.000Z",
  "updated": "2018-10-11T02:02:04.000Z",
  "title": "A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional $p(\\cdot)$-Laplacian",
  "authors": [
    "Ky Ho",
    "Yun-Ho Kim"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain fundamental imbeddings for the fractional Sobolev space with variable exponent that is a generalization of well-known fractional Sobolev spaces. As an application, we obtain a-priori bounds and multiplicity of solutions to some nonlinear elliptic problems involving the fractional $p(\\cdot)$-Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-11T02:02:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear elliptic problems",
      "a-priori bounds",
      "multiplicity",
      "well-known fractional sobolev spaces",
      "fundamental imbeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}