Gradient bounds for a thin film epitaxy equation

Dong Li, Zhonghua Qiao*, Tao Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

15 Citations (Scopus)


We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions d≤3.

Original languageEnglish
Pages (from-to)1720-1746
Number of pages27
JournalJournal of Differential Equations
Issue number3
Publication statusPublished - 5 Feb 2017

Scopus Subject Areas

  • Analysis
  • Applied Mathematics

User-Defined Keywords

  • Epitaxy
  • Gradient bound
  • Maximum principle
  • Thin film


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