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Minimising convex combinations of low eigenvalues∗
Published online by Cambridge University Press: 07 March 2014
Abstract
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.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 2 , April 2014 , pp. 442 - 459
- Copyright
- © EDP Sciences, SMAI, 2014
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