Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface


Journal Article

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. In this work we consider (Formula presented.) which is derived from a thin film equation for epitaxial growth on vicinal surface. We formulate the problem as the gradient flow of a suitably-defined convex functional in a non-reflexive space. Then by restricting it to a Hilbert space and proving the uniqueness of its sub-differential, we can apply the classical maximal monotone operator theory. The mathematical difficulty is due to the fact that whh can appear as a positive Radon measure. We prove the existence of a global strong solution with hidden singularity. In particular, (1) holds almost everywhere when whh is replaced by its absolutely continuous part.

Full Text

Duke Authors

Cited Authors

  • Gao, Y; Liu, JG; Lu, XY; Xu, X

Published Date

  • April 1, 2018

Published In

Volume / Issue

  • 57 / 2

International Standard Serial Number (ISSN)

  • 0944-2669

Digital Object Identifier (DOI)

  • 10.1007/s00526-018-1326-x

Citation Source

  • Scopus