A minimization problem for an elliptic eigenvalue problem with nonlinear dependence on the eigenparameter. (October 2016)

• Record Type: Journal Article
• Authors: Mohammadi, Seyyed Abbas; Voss, Heinrich
• Is Part Of: Nonlinear analysis. Volume 31(2016)
• Page Start: 119
• Page End: 131
• Publication Date: 2016-10
• Subjects: Nonlinear eigenvalue problem -- Shape optimization -- Eigenvalue optimization -- Quantum dots; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.01.015
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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 ) χ D + β ( λ ) χ D c ) ∇ u ) = λ u 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.