# On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique

@article{Brasco2014OnTR, title={On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique}, author={Lorenzo Brasco}, journal={ESAIM: Control, Optimisation and Calculus of Variations}, year={2014}, volume={20}, pages={315-338} }

We generalize to the p -Laplacian
Δ p a spectral inequality proved by M.-T.
Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound
on the first Dirichlet eigenvalue of Δ p of a
set in terms of its p -torsional rigidity. The result is valid in every
space dimension, for every
1 p ∞ and for every open
set with finite measure. Moreover, it holds by replacing the first eigenvalue with more
general optimal Poincare-Sobolev constants. The method of proof…

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