Corpus ID: 221139712

Sharp stability for the interaction energy

  title={Sharp stability for the interaction energy},
  author={Xukai Yan and Yao Yao},
  journal={arXiv: Analysis of PDEs},
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… Expand

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