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 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.

44 pages

References in corpus (1)

• Green's matrices of second order elliptic systems with measurable coefficients in two dimensional domains

Cited by in corpus (4)

• Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity
• The surface diffusion flow with elasticity in the plane
• A gradient flow for the p-elastic energy defined on closed planar curves
• On the Gamma convergence of functionals defined over pairs of measures and energy-measures