INVERSE ITERATION FOR p-GROUND STATES
نویسنده
چکیده
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.
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