We study, in dimension n ≥ 2, the eigenvalue problem and the torsional rigidity for the p-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.
Mots-clés : Nonlinear eigenvalue problems, torsional rigidity, mixed boundary conditions, optimal estimates
@article{COCV_2020__26_1_A111_0,
author = {Paoli, Gloria and Piscitelli, Gianpaolo and Trani, Leonardo},
title = {Sharp estimates for the first $p${\protect\emph{}-Laplacian} eigenvalue and for the $p$\protect\emph{}-torsional rigidity on convex sets with holes},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2020033},
mrnumber = {4185065},
zbl = {1460.35179},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2020033/}
}
TY - JOUR AU - Paoli, Gloria AU - Piscitelli, Gianpaolo AU - Trani, Leonardo TI - Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2020033/ DO - 10.1051/cocv/2020033 LA - en ID - COCV_2020__26_1_A111_0 ER -
%0 Journal Article %A Paoli, Gloria %A Piscitelli, Gianpaolo %A Trani, Leonardo %T Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2020033/ %R 10.1051/cocv/2020033 %G en %F COCV_2020__26_1_A111_0
Paoli, Gloria; Piscitelli, Gianpaolo; Trani, Leonardo. Sharp estimates for the first $p$-Laplacian eigenvalue and for the $p$-torsional rigidity on convex sets with holes. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 111. doi : 10.1051/cocv/2020033. http://www.numdam.org/articles/10.1051/cocv/2020033/
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