Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials

Kyungkeun Kang; Hwa Kil Kim; Tongseok Lim; Geuntaek Seo

doi:10.1007/s00526-020-01882-7

Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials

Kyungkeun Kang, Hwa Kil Kim, Tongseok Lim, Geuntaek Seo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we are concerned with local minimizers of an interaction energy governed by repulsive–attractive potentials of power-law type in one dimension. We prove that sum of two Dirac masses is the unique local minimizer under the λ-Wasserstein metric topology with 1 ≤ λ< ∞, provided masses and distance of Dirac deltas are equally half and one, respectively. In addition, in case of ∞-Wasserstein metric, we characterize stability of steady-state solutions depending on powers of interaction potentials.

Original language	English
Article number	15
Journal	Calculus of Variations and Partial Differential Equations
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/s00526-020-01882-7
Publication status	Published - 2021 Feb

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© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1007/s00526-020-01882-7

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Uniqueness and characterization of local minimizers for the interaction energy with mildly repulsive potentials

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