A famous conjecture made by Lord Rayleigh is the following: “The first eigenvalue of the Laplacian on an open domain of given measure with Dirichlet boundary conditions is minimum when the domain is a ball and only when it is a ball”. This conjecture was proved simultaneously and independently by Faber [G. Faber, Beweiss dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförfegige den leifsten Grundton gibt. Sitz. bayer Acad. Wiss. (1923) 169–172] and Krahn [E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaftdes Kreises. Math. Ann. 94 (1924) 97–100.]. We shall deal with the -Laplacian version of this theorem.
DOI : 10.1051/cocv/2014017
Mots-clés : Symmetry, moving plane method, comparison principles, boundary point lemma
@article{COCV_2015__21_1_60_0,
author = {Chorwadwala, Anisa M.H. and Mahadevan, Rajesh and Toledo, Francisco},
title = {On the {Faber{\textendash}Krahn} inequality for the {Dirichlet} $p${-Laplacian}},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {60--72},
publisher = {EDP-Sciences},
volume = {21},
number = {1},
year = {2015},
doi = {10.1051/cocv/2014017},
zbl = {1319.35145},
mrnumber = {3348415},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2014017/}
}
TY - JOUR AU - Chorwadwala, Anisa M.H. AU - Mahadevan, Rajesh AU - Toledo, Francisco TI - On the Faber–Krahn inequality for the Dirichlet $p$-Laplacian JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 60 EP - 72 VL - 21 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014017/ DO - 10.1051/cocv/2014017 LA - en ID - COCV_2015__21_1_60_0 ER -
%0 Journal Article %A Chorwadwala, Anisa M.H. %A Mahadevan, Rajesh %A Toledo, Francisco %T On the Faber–Krahn inequality for the Dirichlet $p$-Laplacian %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 60-72 %V 21 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014017/ %R 10.1051/cocv/2014017 %G en %F COCV_2015__21_1_60_0
Chorwadwala, Anisa M.H.; Mahadevan, Rajesh; Toledo, Francisco. On the Faber–Krahn inequality for the Dirichlet $p$-Laplacian. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 60-72. doi : 10.1051/cocv/2014017. http://www.numdam.org/articles/10.1051/cocv/2014017/
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