Published 2018
| Submitted + Published
Journal Article
Open
A "Liquid-Solid" Phase Transition in a Simple Model for Swarming, Based on the "No Flat-Spots" Theorem for Subharmonic Functions
- Creators
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Frank, Rupert L.
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Lieb, Elliott H.
Chicago
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Abstract
We consider a family of non-local shape optimization problems, which are motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of different phases for several of them. A technical key ingredient, which we establish, is that a strictly subharmonic function cannot be constant on a set of positive measure.
Additional Information
© 2018 Indiana University Mathematics Journal. The authors are grateful to Luis Silvestre and to Mikhail Sodin for showing us how to prove Proposition A.1 for continuous and for L1 functions, respectively, to Almut Burchard and Paul Gauthier for their careful reading and many helpful comments, and to Haim Brézis for references related to Proposition 2.1. Support by U.S. National Science Foundation grants DMS-1363432 (R.L.F.) and PHY-1265118 (E.H.L.) is acknowledgedAttached Files
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Submitted - 1607.07971.pdf
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Additional details
- Eprint ID
- 89599
- Resolver ID
- CaltechAUTHORS:20180912-155642789
- NSF
- DMS-1363432
- NSF
- PHY-1265118
- Created
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2018-09-12Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field