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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