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

We introduce an iterative method for computing the first eigenpair (λp, ep) for the pLaplacian operator with homogeneous Dirichlet data as the limit of (μq,uq) as q → p −, where uq is the positive solution of the sublinear Lane-Emden equation −∆puq = μqu q−1 q with 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 supersolution which is derived from the solution to the torsional creep problem. Convergence of uq to ep is in the C 1-norm and the rate of convergence of μq to λp is at least O (p− q).