We consider the variational problem inf{αλ1(Ω) + βλ2(Ω) + (1 - α - β)λ3(Ω) | Ω open in ℝn, |Ω| ≤ 1}, for α, β ∈ [0, 1], α + β ≤ 1, where λk(Ω) is the kth eigenvalue of the Dirichlet Laplacian acting in L2(Ω) and |Ω| is the Lebesgue measure of Ω. We investigate for which values of α, β every minimiser is connected.
Mots clés : eigenvalues, Dirichlet-Laplacian, shape optimization
@article{COCV_2014__20_2_442_0,
author = {Iversen, Mette and Mazzoleni, Dario},
title = {Minimising convex combinations of low eigenvalues},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {442--459},
publisher = {EDP-Sciences},
volume = {20},
number = {2},
year = {2014},
doi = {10.1051/cocv/2013070},
mrnumber = {3264211},
zbl = {1290.49096},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2013070/}
}
TY - JOUR AU - Iversen, Mette AU - Mazzoleni, Dario TI - Minimising convex combinations of low eigenvalues JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 442 EP - 459 VL - 20 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2013070/ DO - 10.1051/cocv/2013070 LA - en ID - COCV_2014__20_2_442_0 ER -
%0 Journal Article %A Iversen, Mette %A Mazzoleni, Dario %T Minimising convex combinations of low eigenvalues %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 442-459 %V 20 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2013070/ %R 10.1051/cocv/2013070 %G en %F COCV_2014__20_2_442_0
Iversen, Mette; Mazzoleni, Dario. Minimising convex combinations of low eigenvalues. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 442-459. doi : 10.1051/cocv/2013070. http://archive.numdam.org/articles/10.1051/cocv/2013070/
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