|Publisher DOI:||10.1016/j.nonrwa.2017.09.003||Title:||A nonlinear eigenvalue optimization problem: Optimal potential functions||Language:||English||Authors:||Antunes, Pedro R. S.
Mohammadi, Seyyed Abbas
|Issue Date:||Apr-2018||Source:||Nonlinear Analysis: Real World Applications (40): 307-327 (2018-04)||Abstract (english):||
In 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.
|URI:||http://hdl.handle.net/11420/2996||ISSN:||1468-1218||Institute:||Mathematik E-10||Document Type:||Article||Journal:||Nonlinear analysis|
|Appears in Collections:||Publications without fulltext|
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