A minimization problem for an elliptic eigenvalue problem with nonlinear dependence on the eigenparameter. (October 2016) - Mohammadi, Seyyed Abbas; Voss, Heinrich
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.