Calculus of Variations and Geometric Measure Theory

I. Fonseca - N. Fusco - G. Leoni - M. Morini

Motion of Three-Dimensional Elastic Films by Anisotropic Surface Diffusion with Curvature Regularization

created by morini on 08 May 2014
modified by leoni on 23 May 2014


Submitted Paper

Inserted: 8 may 2014
Last Updated: 23 may 2014

Year: 2014


Short time existence for a surface diffusion evolution equation with curvature regularization is proved in the context of epitaxially strained three-dimensional films. This is achieved by implementing a minimizing movement scheme, which is hinged on the $H^{-1}$-gradient flow structure underpinning the evolution law. Long-time behavior and Liapunov stability in the case of initial data close to a flat configuration are also addressed.

Keywords: minimizing movements, surface diffusion, epitaxial films, Liapunov stability