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

Published online by Cambridge University Press:  06 February 2014

Lorenzo Brasco
Lorenzo Brasco*
Affiliation:
Laboratoire d’Analyse, Topologie, Probabilités, Aix-Marseille Université, 39 Rue Frédéric Joliot Curie, 13453 Marseille Cedex 13, France. [email protected]
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Abstract

We generalize to the p-LaplacianΔp a spectral inequality proved by M.-T.Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower boundon the first Dirichlet eigenvalue of Δp of aset in terms of its p-torsional rigidity. The result is valid in everyspace dimension, for every1 < p < ∞ and for every openset with finite measure. Moreover, it holds by replacing the first eigenvalue with moregeneral optimal Poincaré-Sobolev constants. The method of proof is based on ageneralization of the rearrangement technique introduced by Kohler−Jobin.

Keywords

Torsional rigiditynonlinear eigenvalue problemsspherical rearrangements
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 2 , April 2014 , pp. 315 - 338
Copyright
© EDP Sciences, SMAI, 2014

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