Droplet phase in a nonlocal isoperimetric problem under confinement

We address small volume-fraction asymptotic properties of a nonlocal isoperimetric functional with a confinement term, derived as the sharp interface limit of a variational model for self-assembly of diblock copolymers under confinement by nanoparticle inclusion. We introduce a small parameter $$ \eta $$ to represent the size of the domains of the minority phase, and study the resulting droplet regime as $$ \eta\to 0 $$. By considering …