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

Abstract

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

References in corpus (4)

• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Gradient flow approach to an exponential thin film equation: global existence and latent singularity
• Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface
• Continuum limit of a mesoscopic model with elasticity of step motion on vicinal surfaces