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Minimizers for a one-dimensional interaction energy

Frank, Rupert L. (2022) Minimizers for a one-dimensional interaction energy. Nonlinear Analysis, 216 . Art. No. 112691. ISSN 0362-546X. doi:10.1016/

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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.

Item Type:Article
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URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
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.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)EXC-2111-390814868
Subject Keywords:Minimization problem; Interaction energy; Explicit solution
Record Number:CaltechAUTHORS:20211208-559893000
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Official Citation:Rupert L. Frank, Minimizers for a one-dimensional interaction energy, Nonlinear Analysis, Volume 216, 2022, 112691, ISSN 0362-546X,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112277
Deposited By: George Porter
Deposited On:09 Dec 2021 17:52
Last Modified:01 Feb 2022 22:58

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