The Mullins-Sekerka problem with contact angle

The Mullins-Sekerka problem for closed interfaces is widely studied since it appears naturally as a gradient flow of the area functional, as a sharp interface limit of the Cahn-Hilliard equation, and in physical models of phase changes. In this talk I will address the Mullins-Sekerka problem for interfaces with a ninety degree contact angle. In particular, I will show existence and uniqueness of strong solutions and discuss stability properties. This is joint work with Helmut Abels, Harald Garcke, and Mathias Wilke.