Motion of three-dimensional elastic films by anisotropic surface diffusion with curvature regularization
journal contributionposted on 2015-01-01, 00:00 authored by Irene FonsecaIrene Fonseca, Nicola Fusco, Giovanni LeoniGiovanni Leoni, Massimiliano Morini
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.