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We introduce an iterative method for computing the first eigenpair$(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichletdata as the limit of $(\mu_{q,}u_{q}) $ as $q\rightarrow p^{-}$, where $u_{q}$is the positive solution of the sublinear Lane-Emden equation$-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method isshown to work for any smooth, bounded domain. Solutions to the Lane-Emdenproblem are obtained through inverse iteration of a super-solution which isderived from the solution to the torsional creep problem. Convergence of$u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of$\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence ispresented.

Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions