A minimization problem for an elliptic eigenvalue problem with nonlinear dependence on the eigenparameter

Publikationstyp
Journal Article
Publikationsdatum
2016-10-01
Sprache
English
Author
Mohammadi, Seyyed Abbas 
Voß, Heinrich 
Institut
Mathematik E-10 
TORE-URI
http://hdl.handle.net/11420/5789
Enthalten in
Nonlinear analysis 
Volume
31
Start Page
119
End Page
131
Citation
Nonlinear Analysis: Real World Applications (31): 119-131 (2016-10-01)
Publisher DOI
10.1016/j.nonrwa.2016.01.015
Scopus ID
2-s2.0-84958748568
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.
Schlagworte
Eigenvalue optimization
Nonlinear eigenvalue problem
Quantum dots
Shape optimization
DDC Class
600: Technik