Speaker: Zhonggan Huang (University of Utah: 5th-year PhD student)

 

Title: Regularity of a gradient degenerate Neumann problem and homogenization

 

 

Abstract: I will introduce my recent work with William Feldman about the regularity of a gradient degenerate Neumann problem. The problem arises from the modeling of interfaces such as liquid-air interfaces near a rough solid surface. This problem generalizes the well-studied thin obstacle problem and has some new challenges. In 2D, we can show the same optimal \(C^{1,1/2}\) regularity as the thin obstacle problem with the help of complex analysis. In 3D, we can prove this regularity under some additional constraint. I will explain the key ideas and difficulties in the theory. If time permits, I will also talk about the connection to the homogenization of vertically oscillating Neumann data, which is relevant to the rate-independent pinning phenomenon arising in the motion of droplets on rough surfaces.