Journal of Scientific Computing

, Volume 52, Issue 1, pp 180–201 | Cite as

Computing the First Eigenpair of the p-Laplacian via Inverse Iteration of Sublinear Supersolutions

  • Rodney Josué Biezuner
  • Jed Brown
  • Grey Ercole
  • Eder Marinho Martins
Article

Abstract

We introduce an iterative method for computing the first eigenpair (λp,ep) for the p-Laplacian operator with homogeneous Dirichlet data as the limit of (μq,uq) as qp, where uq is the positive solution of the sublinear Lane-Emden equation \(-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}\) with the same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of uq to ep is in the C1-norm and the rate of convergence of μq to λp is at least O(pq). Numerical evidence is presented.

Keywords

p-Laplacian First eigenvalue and eigenfunction Inverse iteration Lane-Emden problem Torsional creep problem 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Rodney Josué Biezuner
    • 1
  • Jed Brown
    • 2
    • 3
  • Grey Ercole
    • 1
  • Eder Marinho Martins
    • 4
  1. 1.Departamento de Matemática—ICExUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  2. 2.Laboratory of Hydraulics, Hydrology, and Glaciology (VAW)ETH ZürichZürichSwitzerland
  3. 3.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneUSA
  4. 4.Departamento de Matemática—ICEBUniversidade Federal de Ouro PretoOuro PretoBrazil

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