##### Department of Mathematics,

University of California San Diego

****************************

### Math 248 - Analysis Seminar

## William Feldman

#### University of Utah

## Limit shapes of Bernoulli-type free boundaries in periodic media

##### Abstract:

I will discuss some simplified models for the shape of liquid droplets on rough solid surfaces, especially Bernoulli-type free boundary problems. In these models small scale roughness leads to large scale non-uniqueness, hysteresis, and anisotropies. In technical terms we need to understand laminating/foliating families of plane-like solutions, this is related to ideas of Aubry-Mather theory, but, unlike most results in that area, we need to consider local (but not global) energy minimizers.

### November 30, 2021

### 10:00 AM

### https://ucsd.zoom.us/j/99515535778

****************************