{
  "id": "1709.02455",
  "version": "v1",
  "published": "2017-09-07T21:14:20.000Z",
  "updated": "2017-09-07T21:14:20.000Z",
  "title": "A lower bound for the principal eigenvalue of fully nonlinear elliptic operators",
  "authors": [
    "Pablo Blanc"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article we present a new technique to obtain a lower bound for the principal Dirichlet eigenvalue of a fully nonlinear elliptic operator. We ilustrate the construction of an appropriate radial function required to obtain the bound in several examples. In particular we use our results to prove that $\\lim_{p\\to \\infty}\\lambda_{1,p}=\\lambda_{1,\\infty}=\\left(\\frac{\\pi}{2R}\\right)^2$ where $\\lambda_{1,p}$ and $\\lambda_{1,\\infty}$ are the principal eigenvalue for the homogeneous $p$-laplacian and the homogeneous infinity laplacian respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-07T21:14:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "35P30",
      "35J60",
      "35J70"
    ],
    "keywords": [
      "fully nonlinear elliptic operator",
      "lower bound",
      "principal eigenvalue",
      "appropriate radial function",
      "principal dirichlet eigenvalue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}