Calculus of Variations and Geometric Measure Theory

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

Motion of elastic thin films by anisotropic surface diffusion with curvature regularization

created by fuscon on 18 Feb 2011
modified by leoni on 20 May 2014


Published Paper

Inserted: 18 feb 2011
Last Updated: 20 may 2014

Journal: Archive for Rational Mechanics and Analysis
Volume: 205
Pages: 425–466
Year: 2011


Short time existence, uniqueness, and regularity for a surface diffusion evolution equation with curvature regularization are proved in the context of epitaxially strained two-dimensional films. This is achieved by using the $H^{-1}$-gradient flow structure of the evolution law, via De Giorgi's minimizing movements. This seems to be the first short time existence result for a surface diffusion type geometric evolution equation in the presence of elasticity.

Keywords: minimizing movements, Epitaxially strained elastic films, Surface diffusion