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

Publication
, Journal Article

Gao, Y; Liu, JG; Lu, XY; Xu, X

Published in: Calculus of Variations and Partial Differential Equations

April 1, 2018

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.

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## Published In

Calculus of Variations and Partial Differential Equations

## DOI

## ISSN

0944-2669

## Publication Date

April 1, 2018

## Volume

57

## Issue

2

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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MLA

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Gao, Y., Liu, J. G., Lu, X. Y., & Xu, X. (2018). Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface.

*Calculus of Variations and Partial Differential Equations*,*57*(2). https://doi.org/10.1007/s00526-018-1326-xGao, Y., J. G. Liu, X. Y. Lu, and X. Xu. “Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface.”

*Calculus of Variations and Partial Differential Equations*57, no. 2 (April 1, 2018). https://doi.org/10.1007/s00526-018-1326-x.Gao Y, Liu JG, Lu XY, Xu X. Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface. Calculus of Variations and Partial Differential Equations. 2018 Apr 1;57(2).

Gao, Y., et al. “Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface.”

*Calculus of Variations and Partial Differential Equations*, vol. 57, no. 2, Apr. 2018.*Scopus*, doi:10.1007/s00526-018-1326-x.Gao Y, Liu JG, Lu XY, Xu X. Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface. Calculus of Variations and Partial Differential Equations. 2018 Apr 1;57(2).

## Published In

Calculus of Variations and Partial Differential Equations

## DOI

## ISSN

0944-2669

## Publication Date

April 1, 2018

## Volume

57

## Issue

2

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics