We examine a class of step ow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. ur goal is to derive a consistent contin uummodel for the ev olutionof the lm surface. Away from peaks and valleys, the surface height solves a Hamilton- acobi equation (H E). he peaks are free boundaries for this H E. heir evolution must be speci ed by boundary conditions re ecting the microscopic physics of nucleation. e investigate this boundary condition by numerical simulation of the step ow dynamics using a simple n ucleationlaw. ur results rev ealthe presence of sp ecial structures in the pro le near a peak; we discuss the relationship between these structures and the contin uumequation. e further address the importance of ev aporationfor matching the local behavior near the peak to the solution of the contin uum equation.