Droplet solutions in the diblock copolymer problem with skewed monomer composition (Q818843)

A diblock copolymer molecule is a linear sub-chain of \(N_{A}\) A-monomers grafted covalently to another sub-chain of \(N_{B}\) B-monomers. The paper deals with the case when \(N_{A}\) and \(N_{B}\) are large but with different orders of magnitude. In order to obtain their main result regarding the existence and the definition of the free energy of the local minimizer, the author uses a Lyapunov-Schmidt reduction approach combined with the constructing of a manifold of approximate solutions together with its fibers, and the fiber solution is connected to the variational structure of the free energy.