Calculus of Variations and Geometric Measure Theory

A. Burchard - D. Carazzato - I. Topaloglu

Maximizers of nonlocal interactions of Wasserstein type

created by carazzato on 12 Sep 2023



Inserted: 12 sep 2023

Year: 2023

ArXiv: 2309.05522 PDF


We characterize the maximizers of a functional involving the minimization of the Wasserstein distance between equal volume sets. This functional appears as a repulsive interaction term in some models describing biological membranes. We combine a symmetrization-by-reflection technique with the uniqueness of optimal transport plans to prove that balls are the only maximizers. Further, in one dimension, we provide a sharp quantitative version of this maximality result.