ORCID: https://orcid.org/0000-0001-7973-4688 and 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
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 |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 0022-2518 |
Language: | English |
Item ID: | 66378 |
Date Deposited: | 19. Jul 2019, 12:19 |
Last Modified: | 13. Aug 2024, 12:42 |