Antunes, Pedro R. S.Mohammadi, Seyyed AbbasVoss, Heinrich2018-02-262019-04-012018-041468-1218http://hdl.handle.net/10400.2/7176In this paper we study the following optimal shape design problem: Given an open connected set Ω⊂RN and a positive number A∈(0,|Ω|), find a measurable subset D⊂Ω with |D|=A such that the minimal eigenvalue of −div(ζ(λ,x)∇u)+αχDu=λu in Ω, u=0 on ∂Ω, is as small as possible. This sort of nonlinear eigenvalue problems arises in the study of some quantum dots taking into account an electron effective mass. We establish the existence of a solution and we determine some qualitative aspects of the optimal configurations. For instance, we can get a nearly optimal set which is an approximation of the minimizer in ultra-high contrast regime. A numerical algorithm is proposed to obtain an approximate description of the optimizer.engNonlinear eigenvalue problemShape optimizationUltra-high contrast regimeQuantum dotsjournal articlehttps://doi.org/10.1016/j.nonrwa.2017.09.003