{
  "id": "1512.04770",
  "version": "v1",
  "published": "2015-12-15T13:05:58.000Z",
  "updated": "2015-12-15T13:05:58.000Z",
  "title": "Mixed eigenvalues of p-Laplacian on trees",
  "authors": [
    "LingDi Wang"
  ],
  "comment": "17 pages. arXiv admin note: substantial text overlap with arXiv:1304.5310",
  "categories": [
    "math.PR",
    "math.SP"
  ],
  "abstract": "We consider the principal eigenvalue of discrete p-Laplacian ($p\\geqslant2$) on the set of trees with unique root $o$. Alternatively, it is study the optimal constant of a class of weighted Hardy inequality. The main goal is estimating the eigenvalue (i.e., the optimal constant of the Hardy inequality) with Dirichlet boundary at unique root $o$. Three kinds of variational formulas for the eigenvalue are presented. As applications of these formulas, we obtain a criterion for positivity of the eigenvalue on a tree with finite vertexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-15T13:05:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mixed eigenvalues",
      "optimal constant",
      "unique root",
      "principal eigenvalue",
      "main goal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151204770W"
    }
  }
}