On The Spectra Of Three-Dimensional Lamellar Solutions Of The Diblock Copolymer Problem

One-dimensional free energy local minimizers are viewed as three-dimensional lamellar-type critical points in a box. To determine whether they model the lamellar phase of diblock copolymers in the strong segregation region, we analyze their spectra. We obtain the asymptotic expansions of their eigenvalues and eigenfunctions. Consequently we find that they are stable, i.e., are local minimizers in space, only if they have sufficiently many interfaces. Interestingly the one-dimensional global minimizer is near the borderline of three-dimensional stability.