2024/12/28 by Ruiwen Shu, Shu, Ruiwen
Mathematics · #31B15 #49K20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2412.20248
openalex publication_date 2024/12/28 · openalex created_date 2025/01/01 · openalex updated_date 2026/07/28
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.