{
  "id": "0903.4464",
  "version": "v1",
  "published": "2009-03-25T20:45:27.000Z",
  "updated": "2009-03-25T20:45:27.000Z",
  "title": "Estimates on Pull-in Distances in MEMS Models and other Nonlinear Eigenvalue Problems",
  "authors": [
    "Nassif Ghoussoub",
    "Craig Cowan"
  ],
  "comment": "17 pages. Updated versions --if any-- of this author's papers can be downloaded at http://www.birs.ca/~nassif/",
  "categories": [
    "math.AP"
  ],
  "abstract": "Motivated by certain mathematical models for Micro-Electro-Mechanical Systems (MEMS), we give upper and lower $L^\\infty$ estimates for the minimal solutions of nonlinear eigenvalue problems of the form $-\\Delta u = \\lambda f(x) F(u)$ on a smooth bounded domain $ \\Omega$ in $\\IR^N$. We are mainly interested in the {\\it pull-in distance}, that is the $L^\\infty-$norm of the extremal solution $u^*$ and how it depends on the geometry of the domain, the dimension of the space, and the so-called {\\it permittivity profile} $f$. In particular, our results provide mathematical proofs for various observed phenomena, as well as rigorous derivations for several estimates obtained numerically by Pelesko \\cite{P}, Guo-Pan-Ward \\cite{GPW} and others in the case of the MEMS non-linearity $F(u)=\\frac{1}{(1-u)^2}$ and for power-law permittivity profiles $f(x)=|x|^\\alpha$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-25T20:45:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear eigenvalue problems",
      "pull-in distance",
      "mems models",
      "power-law permittivity profiles",
      "minimal solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.4464G"
    }
  }
}