Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222285 | Nonlinear Analysis: Real World Applications | 2016 | 13 Pages |
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 âdiv((α(λ)ÏD+β(λ)ÏDc)âu)=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.
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Authors
Seyyed Abbas Mohammadi, Heinrich Voss,