Minimising convex combinations of low eigenvalues∗. (7th April 2014)

• Record Type: Journal Article
• Authors: Iversen, Mette; Mazzoleni, Dario
• Is Part Of: ESAIM. Volume 20:Number 2(2014:Apr.)
• Page Start: 442
• Page End: 459
• Publication Date: 2014-04-07
• Subjects: Eigenvalues, -- Dirichlet–Laplacian, -- Shape Optimization; System analysis -- Periodicals; Calculus of variations -- Periodicals; Mathematical analysis -- Periodicals; Mathematical optimization -- Periodicals; Control theory -- Periodicals; 515.64
• DOI: 10.1051/cocv/2013070
• Languages: English
• ISSNs: 1292-8119

Abstract

Abstract : We consider the variational problem inf{ αλ 1 ( Ω ) + βλ 2 ( Ω ) + (1 − α − β ) λ 3 ( Ω ) | Ω open in ℝ n, | Ω | ≤ 1}, for α, β ∈ [0, 1], α + β ≤ 1, where λ k ( Ω ) is the k th eigenvalue of the Dirichlet Laplacian acting in L 2 ( Ω ) and | Ω | is the Lebesgue measure of Ω . We investigate for which values of α, β every minimiser is connected.