Minimising convex combinations of low eigenvalues∗. (7th April 2014) - Iversen, Mette; Mazzoleni, Dario
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.