A `liquid-solid' phase transition in a simple model for swarming

Rupert L. Frank, Elliott H. Lieb

Published 2016-07-27Version 1

We consider a non-local shape optimization problem, which is motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of different phases. A technical key ingredient, which we establish, is that a strictly subharmonic function cannot be constant on a set of positive measure.