Droplet solutions in the diblock copolymer problem with skewed monomer composition

Original Article

DOI: 10.1007/s00526-005-0345-6

Cite this article as:
Ren, X. & Wei, J. Calc. Var. (2006) 25: 333. doi:10.1007/s00526-005-0345-6


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.

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUtah State University LoganUSA
  2. 2.Department of MathematicsChinese University of Hong KongHong KongPRC

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