Uniform energy and density distribution: diblock copolymers' functional
Summary: We study a nonlocal variational problem arising in diblock copolymers models, whose energy is given by the Cahn-Hilliard functional plus a long-range interaction term. We prove that minimizers develop uniform energy and density distributions, thus justifying partially the highly regular microphase separation observed in diblock copolymers' melts. We also give a new proof of the scaling law for the minimum energy. This work extends the techniques introduced by \textit{G. Alberti, R. Choksi} and \textit{F. Otto} [J. Am. Math. Soc. 22, 569--605 (2009; doi:10.1090/S0894-0347-08-00622-X)] where analogous results are proved for the sharp interface limit of the functional considered.
scientific article; zbMATH DE number 5654752