Gradient Bounds and Coarsening Estimates for Some Molecular Beam Epitaxy Models

TL;DR

This paper establishes global well-posedness and gradient bounds for molecular beam epitaxy models, providing insights into the solutions' regularity and roughness over time.

Contribution

It introduces new gradient and roughness bounds for molecular beam epitaxy models, advancing understanding of their long-term behavior.

Findings

Proved global well-posedness of certain models

Derived bounds on the gradient of solutions

Established global bounds on solution roughness

Abstract

We prove global well-posedness for some molecular beam epitaxy models. This requires proving some bounds on the gradient of solutions. We also obtain some global bounds on the roughness of solutions.