A ‘liquid-solid’ Phase Transition in a Simple Model for Swarming, Based on the ‘no Flat-spots’ Theorem for Subharmonic Functions
نویسندگان
چکیده
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.
منابع مشابه
A ‘liquid-solid’ Phase Transition in a Simple Model for Swarming
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.
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