# 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}
}```
• L. Brasco
• Published 1 April 2014
• Mathematics
• ESAIM: Control, Optimisation and Calculus of Variations
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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