Regularity and monotonicity for solutions to a continuum model of epitaxial growth with nonlocal elastic effects

We study a nonlocal 4th order degenerate equation deriving from the epitaxial growth on crystalline materials. first prove global existence of evolution variational inequality solution with general initial data using gradient flow structure. Then monotone data, we subdifferential associated convex functional is indeed single-valued, which gives higher regularities solution. Particularly, regularites imply that strict monotonicity maintains for all time, provides rigorous justification global-in time to model elastic effects vicinal surface.