Antunes, Pedro R. S.Pedro R. S.AntunesMohammadi, Seyyed AbbasSeyyed AbbasMohammadiVoß, HeinrichHeinrichVoß2019-07-192019-07-192018-04Nonlinear Analysis: Real World Applications (40): 307-327 (2018-04)http://hdl.handle.net/11420/2996In 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.en1468-12182018307327Journal Article10.1016/j.nonrwa.2017.09.003Journal Article