{
  "id": "1309.6454",
  "version": "v1",
  "published": "2013-09-25T10:23:32.000Z",
  "updated": "2013-09-25T10:23:32.000Z",
  "title": "Principal eigenvalue of the fractional Laplacian with a large incompressible drift",
  "authors": [
    "Krzysztof Bogdan",
    "Tomasz Komorowski"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AP",
    "math.FA",
    "math.PR"
  ],
  "abstract": "We add a divergence-free drift with increasing magnitude to the fractional Laplacian on a bounded smooth domain, and discuss the behavior of the principal eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and only if the drift has non-trivial first integrals in the domain of the quadratic form of the fractional Laplacian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-25T10:23:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B09",
      "47G20",
      "60J75"
    ],
    "keywords": [
      "fractional laplacian",
      "large incompressible drift",
      "principal eigenvalue",
      "non-trivial first integrals",
      "quadratic form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6454B"
    }
  }
}