  In modeling phase transitions, it is useful to be able to connect diffuse
interface descriptions of the dynamics with corresponding limiting sharp
interface motions. In the case of the deep quench obstacle problem (DQOP) and
surface diffusion (SD), while a formal connection was demonstrated many years
ago, rigorous proof of the connection has yet to be established. In the present
note, we show how information regarding the steady states for both these
motions can provide insight into the dynamic connection, and we outline tools
that should enable further progress. For simplicity, we take both motions to be
defined on a planar disk.
