Minimising convex combinations of low eigenvalues
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 2, pp. 442-459.

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.

DOI : 10.1051/cocv/2013070
Classification : 49Q10, 49R50, 35P15
Mots clés : eigenvalues, Dirichlet-Laplacian, shape optimization
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     title = {Minimising convex combinations of low eigenvalues},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {442--459},
     publisher = {EDP-Sciences},
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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://www.numdam.org/articles/10.1051/cocv/2013070/

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