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

Lorenzo Brasco (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We generalize to the p-Laplacian 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 rst Dirichlet eigenvalue of p of a set in terms of its p-torsional rigidity. The result is valid in every space dimension, for every 1 < p < 1 and for every open set having nite measure. Moreover, it holds by replacing the rst eigenvalue with more general optimal Poincar e-Sobolev constants. The method of proof is based on a generalization of the rearrangement technique introduced by Kohler-Jobin.

Mots clés: Torsional rigidity; nonlinear eigenvalue problems; spherical rearrangements

Domaines: Equations aux dérivées partielles [math.AP]

Lorenzo Brasco. On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique. 2013. ⟨hal-00783875⟩