# Analysis Seminar

## On the existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains

Bohan Zhou, Dartmouth College

Friday, November 6th, 2020
1:00 PM - 2:00 PM
Zoom ID 5059122491

The isoperimetric-type problem is an archetypical problem in the geometric measure theory. It often corresponds to some energy minimization and ties with calculus of variation. In this talk, we study an open double minimization problem in unbounded domains proposed by Buttazzo, Carlier and Laborde. To model lipid bilayer membranes, the minimization problem consists of one perimeter term, which represents the interfacial energy, and $p$-Wasserstein distance, which represents the covalent bonding energy. They prove the existence in 2D and propose it holds in high dimensions. We provide a new approach to this problem in any dimension and prove the existence of optimal solutions for $\mathbb{R}^d$, $\frac{1}{p}+\frac{2}{d}>1$ and small constrained volumes. Furthermore, minimizers are proved to be bounded sets, thus the regularity results follow from classical references. This is a joint work with my PhD advisor Prof. Qinglan Xia.

Event contact: dan dot geba at rochester dot edu