This talk addresses aspects of a classic question in epitaxial growth:
May facets of evolving crystal surfaces be described by
fully continuum models? A difficulty in the use of traditional, PDE-based
approaches for this problem lies in the development of (time-dependent)
singularities of continuum solutions in the vicinity of the facet;
such singularities may indicate the breakdown
of the continuum theory. By invoking an evaporation model
for line defects (steps) of crystal surfaces, I discuss the connection
of a fully continuum variational approach for facets to the underlying microstructure.
This is joint work with Kanna Nakamura.