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dirichlet–laplacian

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Minimising convex combinations of low eigenvalues ∗
Mette Iversen, Dario Mazzoleni
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 2 / April 2014

Published online by Cambridge University Press:

07 March 2014, pp. 442-459

Print publication:

April 2014
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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.