标题： 吸引-排斥相互作用能量极小化的径向对称性破坏 显示英文标题

标题： Break of radial symmetry for a class of attractive-repulsive interaction energy minimizers

摘要： 径向对称性的破坏是相互作用能量极小值的一个现象，其中径向相互作用势能的极小值从不具有径向对称性。 在数值上，对于各种类型的相互作用势能，这一现象已被频繁观察到，然而对此现象的严格证明仅在非常有限的情况下完成。 我们提出了一种新的方法来证明径向对称性的破坏，通过使用径向概率测度类中的能量下界，并结合构造一个能量低于该下界的概率测度。 特别是，我们证明了对于一类在短距离处为排斥性而在长距离处为吸引力的相互作用势能，每一个能量极小值都必然是一个不具有径向对称性的霍尔德连续函数。 显示英文摘要

摘要： 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 H\"older continuous function which is not radially symmetric.