论文标题
相互作用能量的急剧稳定性
Sharp stability for the interaction energy
论文作者
论文摘要
本文致力于对相互作用能量的稳定性估计，并严格降低了相互作用电位，例如库仑和瑞斯电位。对于一般密度函数，我们首先证明了密度的$ l^1 $不对称性，从而扩展了Burchard-Chambers，Frank-Lieb和Fusco-Pratelli的一些先前结果，以实现特征功能。我们还根据密度与径向减少重排之间的2-wasserstein距离获得了稳定性估计。最后，我们考虑了牛顿潜力的特殊情况，并探讨了郭关于库仑能量的稳定性的猜想。
This paper is devoted to stability estimates for the interaction energy with strictly radially decreasing interaction potentials, such as the Coulomb and Riesz potentials. For a general density function, we first prove a stability estimate in terms of the $L^1$ asymmetry of the density, extending some previous results by Burchard-Chambers, Frank-Lieb and Fusco-Pratelli for characteristic functions. We also obtain a stability estimate in terms of the 2-Wasserstein distance between the density and its radial decreasing rearrangement. Finally, we consider the special case of Newtonian potential, and address a conjecture by Guo on the stability for the Coulomb energy.
