Continuum limit of a mesoscopic model with elasticity of step motion on   vicinal surfaces
  This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. Appl. Math. 2002]. We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first order convergence rate. 
Yuan Gao, Jian-Guo Liu, Jianfeng Lu
math.AP nlin.AO