MOTION OF THREE-DIMENSIONAL ELASTIC FILMS BY ANISOTROPIC SURFACE DIFFUSION WITH CURVATURE REGULARIZATION

Abstract. Short time existence for a surface diffusion evolution equation with curvature regu-larization 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