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 ∈ (1, ∞) and a given domain Ω ⊂ ℝⁿ, we analyze a scheme that allows us to approximate the smallest value the ratio ∫_Ω |Dψ|^pdx/ ∫ _Ω|ψ|^pdx can assume for functions ψ that vanish on ∂Ω. The scheme in question also provides a natural way to approximate minimizing ψ. Our analysis also extends in the limit as p → ∞ and thereby fashions a new approximation method for ground states of the infinity Laplacian. [ABSTRACT FROM AUTHOR]