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# Shell structure as solution to a free boundary problem from block copolymer morphology

• A shell like structure is sought as a solution of a free boundary problem derived from the Ohta-Kawasaki theory of diblock copolymers. The boundary of the shell satisfies an equation that involves its mean curvature and the location of the entire shell. A variant of Lyapunov-Schmidt reduction process is performed that rigorously reduces the free boundary problem to a finite dimensional problem. The finite dimensional problem is solved numerically. The problem has two parameters: $a$ and $\gamma$. When $a$ is small, there are a lower bound and a sequence such that if $\gamma$ is greater than the lower bound and stays away from the sequence, there is a shell like solution.
Mathematics Subject Classification: 35R35, 82B24, 82D60.

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