Minimizers for a one-dimensional interaction energy

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.

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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Published - 1-s2.0-S0362546X21002716-main.pdf

Accepted Version - 2109.08929.pdf

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