Publisher DOI: 10.1016/j.nonrwa.2016.01.015
Title: A minimization problem for an elliptic eigenvalue problem with nonlinear dependence on the eigenparameter
Language: English
Authors: Mohammadi, Seyyed Abbas 
Voß, Heinrich 
Keywords: Eigenvalue optimization;Nonlinear eigenvalue problem;Quantum dots;Shape optimization
Issue Date: 1-Oct-2016
Source: Nonlinear Analysis: Real World Applications (31): 119-131 (2016-10-01)
Abstract (english): 
In this paper we examine an eigenvalue optimization problem. Given two nonlinear functions α(λ) and β(λ), find a subset D of the unit ball of measure A for which the first Dirichlet eigenvalue of the operator -div((α(λ)χD+β(λ)χDc)∇ u)=λu 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 propose a numerical algorithm to obtain an approximate description of the optimizer.
URI: http://hdl.handle.net/11420/5789
ISSN: 1468-1218
Institute: Mathematik E-10 
Document Type: Article
Journal: Nonlinear analysis 
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