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In modeling phase transitions, it is useful to be able to connect diffuseinterface descriptions of the dynamics with corresponding limiting sharpinterface motions. In the case of the deep quench obstacle problem (DQOP) andsurface diffusion (SD), while a formal connection was demonstrated many yearsago, rigorous proof of the connection has yet to be established. In the presentnote, we show how information regarding the steady states for both thesemotions can provide insight into the dynamic connection, and we outline toolsthat should enable further progress. For simplicity, we take both motions to bedefined on a planar disk.

Connecting the Deep Quench Obstacle Problem with Surface Diffusion via their Steady States