| Frank, Rupert L.; Lieb, Elliott H. (2018): A "Liquid-Solid" Phase Transition in a Simple Model for Swarming, Based on the "No Flat-Spots" Theorem for Subharmonic Functions. In: Indiana University Mathematics Journal, Vol. 67, No. 4: pp. 1547-1569 |
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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.
| Item Type: | Journal article |
|---|---|
| Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
| Subjects: | 500 Science > 510 Mathematics |
| ISSN: | 0022-2518 |
| Language: | English |
| ID Code: | 66378 |
| Deposited On: | 19. Jul 2019 12:19 |
| Last Modified: | 19. Jul 2019 12:19 |
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