On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique
ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 2, p. 315-338

We generalize to the p-Laplacian Δp 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 Δp 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 Poincaré-Sobolev constants. The method of proof is based on a generalization of the rearrangement technique introduced by Kohler-Jobin.

DOI : https://doi.org/10.1051/cocv/2013065
Classification:  35P30,  47A75,  49Q10
Keywords: torsional rigidity, nonlinear eigenvalue problems, spherical rearrangements
@article{COCV_2014__20_2_315_0,
     author = {Brasco, Lorenzo},
     title = {On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {2},
     year = {2014},
     pages = {315-338},
     doi = {10.1051/cocv/2013065},
     zbl = {1290.35160},
     mrnumber = {3264206},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2014__20_2_315_0}
}
Brasco, Lorenzo. On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 2, pp. 315-338. doi : 10.1051/cocv/2013065. http://www.numdam.org/item/COCV_2014__20_2_315_0/

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