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arXiv · 1607.07971

A `liquid-solid' phase transition in a simple model for swarming, based on the `no flat-spots' theorem for subharmonic functions

Rupert L. Frank·Elliott H. Lieb
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Abstract

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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Rupert L. Frank, Elliott H. Lieb. 2016-07-27. A `liquid-solid' phase transition in a simple model for swarming, based on the `no flat-spots' theorem for subharmonic functions. https://arxiv.org/abs/1607.07971

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