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

TL;DR

This paper establishes the global existence and regularity of solutions to a nonlocal fourth-order degenerate PDE modeling epitaxial growth, demonstrating the preservation of monotonicity over time.

Contribution

It proves global existence of solutions using gradient flow structure and shows monotonicity preservation, providing rigorous justification for the model's behavior.

Findings

Global existence of solutions established

Higher regularity and monotonicity preservation proved

Rigorous justification for monotone solutions in epitaxial growth

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.