{
  "id": "1304.6988",
  "version": "v1",
  "published": "2013-04-25T19:39:03.000Z",
  "updated": "2013-04-25T19:39:03.000Z",
  "title": "Lyapunov-type Inequalities for Partial Differential Equations",
  "authors": [
    "Pablo L. De Nápoli",
    "Juan P. Pinasco"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the $p-$Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the $p-$Laplacian, and compare them with the usual ones in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-25T19:39:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P15",
      "35P30"
    ],
    "keywords": [
      "partial differential equations",
      "lyapunov-type inequalities",
      "quasilinear elliptic differential operators",
      "zero dirichlet boundary condition",
      "degenerate elliptic problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.6988D"
    }
  }
}