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

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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
Keywords: eigenvalues, Dirichlet-Laplacian, shape optimization 
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     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://geodesic.mathdoc.fr/articles/10.1051/cocv/2013070/}
}
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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

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