Extremal eigenvalue problems for composite membranes. II
This work is a continuation of a paper with the same title [part I: see the foregoing entry (Zbl 0709.73044)]. The optimality conditions are obtained as an immediate consequence of a minimum principle. A direct approach is taken to characterize the solution of the optimal design problem. This characterization allows to use the linear membrane equation in the form of a nonlinear eigenvalue problem. From this the results are obtained on the geometry of the level sets of eigenfunctions and subsequently on the geometry of the extremizers of \(\rho \to \lambda_ 1(\rho)\).
scientific article; zbMATH DE number 4167169
scientific article