  We study the continuum limit of a family of kinetic Monte Carlo models of
crystal surface relaxation that includes both the solid-on-solid and discrete
Gaussian models. With computational experiments and theoretical arguments we
are able to derive several partial differential equation limits identified (or
nearly identified) in previous studies and to clarify the correct choice of
surface tension appearing in the PDE and the correct scaling regime giving rise
to each PDE. We also provide preliminary computational investigations of a
number of interesting qualitative features of the large scale behavior of the
models.
