Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024359 | Nonlinear Analysis: Real World Applications | 2018 | 21 Pages |
Abstract
In this paper we study the following optimal shape design problem: Given an open connected set ΩâRN and a positive number Aâ(0,|Ω|), find a measurable subset DâΩ with |D|=A such that the minimal eigenvalue of âdiv(ζ(λ,x)âu)+αÏDu=λu in Ω, u=0 on âΩ, 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.
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Authors
Pedro R.S. Antunes, Seyyed Abbas Mohammadi, Heinrich Voss,