Droplet solutions in the diblock copolymer problem with skewed monomer composition
- First Online:
- Cite this article as:
- Ren, X. & Wei, J. Calc. Var. (2006) 25: 333. doi:10.1007/s00526-005-0345-6
- 40 Downloads
A droplet solution characterizes the lamellar phase of a diblock copolymer when the two composing monomers maintain a skewed ratio. We study the threshold case where the free energy of a droplet solution is comparable to the free energy of the constant solution. Using a Lyapunov-Schmidt reduction approach, adapted to calculus of variations, we prove the existence of a free energy local minimizer with a given number of droplets. Also determined are the free energy, the droplet location, and the droplet size.