A Variational model involving nonlocal interactions of Wasserstein type

by Prof. Ihsan Topaloglu (Virginia Commonwealth University, USA)

Thursday 21 Mar 2024, 17:00 → 18:00 Europe/Rome

Aula Riunioni (Department of Mathematics)

In this talk I will consider a variational problem which appears in models of bilayer membranes. After introducing and deriving the model I will establish the existence of volume-constrained minimizers where the energy functional consists of two competing terms: a surface energy term penalizing transitions between sets and a nonlocal energy involving the Wasserstein distance between equal volume sets. In the second part of the talk I will consider the maximization of the minimum Wasserstein distance between two given sets, and show that this maximum is obtained by a micella. These results are drawn from joint works with Almut Burchard, Davide Carazzato, Michael Novack, and Raghavendra Venkatraman.