Evolution of elastic thin films with curvature regularization via minimizing movements

The evolution equation with curvature regularization that models the motion 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.