Inverse iteration for $p$-ground states

We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for $p\in (1,\mathrm{\infty })$ and a given domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$, we analyze a scheme that allows us to approximate the smallest value the ratio $\int_\Omega|D\psi|^p dx/\int_\Omega|\psi|^p dx$canassumeforfunctions$\psi$thatvanishon$\partial \Omega$. The scheme in question also provides a natural way to approximate minimizing $\psi$. Our analysis also extends in the limit as $p\to \mathrm{\infty }$ and thereby fashions a new approximation method for ground states of the infinity Laplacian.