{
  "id": "1907.11455",
  "version": "v1",
  "published": "2019-07-26T09:34:54.000Z",
  "updated": "2019-07-26T09:34:54.000Z",
  "title": "Non-local to local transition for ground states of fractional Schrödinger equations on bounded domains",
  "authors": [
    "Bartosz Bieganowski",
    "Simone Secchi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that ground state solutions to the nonlinear, fractional problem \\begin{align*} \\left\\{ \\begin{array}{ll} (-\\Delta)^{s} u + V(x) u = f(x,u) &\\quad \\mathrm{in} \\ \\Omega, \\newline u = 0 &\\quad \\mathrm{in} \\ \\mathbb{R}^N \\setminus \\Omega, \\end{array} \\right. \\end{align*} on a bounded domain $\\Omega \\subset \\mathbb{R}^N$, converge (along a subsequence) in $L^2 (\\Omega)$, under suitable conditions on $f$ and $V$, to a solution of the local problem as $s \\to 1^-$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-26T09:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A15",
      "35R11"
    ],
    "keywords": [
      "fractional schrödinger equations",
      "bounded domain",
      "local transition",
      "ground state solutions",
      "local problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}