Frank, Rupert L. (2022) Minimizers for a one-dimensional interaction energy. Nonlinear Analysis, 216 . Art. No. 112691. ISSN 0362-546X. doi:10.1016/j.na.2021.112691. https://resolver.caltech.edu/CaltechAUTHORS:20211208-559893000
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Abstract
We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modeling of aggregation phenomena. We show that in a certain regime minimizers are absolutely continuous with an unbounded density, thereby settling a question that was left open in previous works.
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| Additional Information: | © 2021 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes. Received 18 September 2021, Accepted 4 November 2021, Available online 3 December 2021. Partial support through U.S. National Science Foundation grant DMS-1954995 and through the Deutsche Forschungsgemeinschaft (German Research Foundation) through Germany’s Excellence Strategy EXC-2111-390814868 is acknowledged. | |||||||||
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| Subject Keywords: | Minimization problem; Interaction energy; Explicit solution | |||||||||
| DOI: | 10.1016/j.na.2021.112691 | |||||||||
| Record Number: | CaltechAUTHORS:20211208-559893000 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20211208-559893000 | |||||||||
| Official Citation: | Rupert L. Frank, Minimizers for a one-dimensional interaction energy, Nonlinear Analysis, Volume 216, 2022, 112691, ISSN 0362-546X, https://doi.org/10.1016/j.na.2021.112691. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 112277 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 09 Dec 2021 17:52 | |||||||||
| Last Modified: | 01 Feb 2022 22:58 |
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