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

Lorenzo Brasco — 2014

ESAIM: Control, Optimisation and Calculus of Variations

We generalize to the -Laplacian 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 of a set in terms of its -torsional rigidity. The result is valid in every space dimension, for every 1    ∞ and for every open set with finite measure. Moreover, it holds by replacing the first eigenvalue with more general optimal Poincaré-Sobolev constants. The method...

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