On variational scheme modeling the anisotropic surface diffusion with elasticity in the plane

In this paper, we prove the existence of classical solutions for the anisotropic surface diffusion with elasticity in the plane using a minimizing movements scheme, provided that the initial set is sufficiently regular. This scheme is inspired by the one introduced by Cahn-Taylor [15] to modeling the surface diffusion. Moreover, we prove that this scheme converges to the global solution of the equation.