Break of radial symmetry for a class of attractive-repulsive interaction energy minimizers
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916546025095168 |
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| author | Shu, Ruiwen |
| author_facet | Shu, Ruiwen |
| contents | Break of radial symmetry for interaction energy minimizers is a phenomenon where a radial interaction potential whose associated energy minimizers are never radially symmetric. Numerically, it has been frequently observed for various types of interaction potentials, however, rigorous justification of this phenomenon was only done in very limited cases. We propose a new approach to prove the break of radial symmetry, by using a lower bound for the energy in the class of radial probability measures, combining with the construction of a probability measure whose energy is lower than this lower bound. In particular, we prove that for a class of interaction potentials that are repulsive at short distance and attractive at long distance, every energy minimizer is necessarily a Hölder continuous function which is not radially symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Break of radial symmetry for a class of attractive-repulsive interaction energy minimizers Shu, Ruiwen Analysis of PDEs Mathematical Physics Classical Analysis and ODEs 31B15, 49K20 Break of radial symmetry for interaction energy minimizers is a phenomenon where a radial interaction potential whose associated energy minimizers are never radially symmetric. Numerically, it has been frequently observed for various types of interaction potentials, however, rigorous justification of this phenomenon was only done in very limited cases. We propose a new approach to prove the break of radial symmetry, by using a lower bound for the energy in the class of radial probability measures, combining with the construction of a probability measure whose energy is lower than this lower bound. In particular, we prove that for a class of interaction potentials that are repulsive at short distance and attractive at long distance, every energy minimizer is necessarily a Hölder continuous function which is not radially symmetric. |
| title | Break of radial symmetry for a class of attractive-repulsive interaction energy minimizers |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs 31B15, 49K20 |
| url | https://arxiv.org/abs/2412.20248 |