Calculus of Variations and Geometric Measure Theory

P. Piovano

Evolution of elastic thin films with curvature regularization via minimizing movements

created by piovano on 28 Aug 2016


Published Paper

Inserted: 28 aug 2016
Last Updated: 28 aug 2016

Journal: Calc. Var. Partial Differential Equations
Volume: 49
Pages: 337-367
Year: 2014


The evolution equation with curvature regularization that models the mo- tion of a two-dimensional thin film by evaporation-condensation on a rigid substrate is considered. The film is strained due to the mismatch between the crystalline lattices of the two materials. Here, short time existence, uniqueness and regularity of the solution are established using De Giorgi’s minimizing movements to exploit the $L^2$-gradient flow structure of the equation. This seems to be the first analytical result for the evaporation- condensation case in the presence of elasticity.

Keywords: evolution, Gradient Flow, minimizing movements, elasticity, anisotropy, motion by mean curvature, thin film, epitaxy, evaporation-condensation, grain boundaries