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

TL;DR

This paper establishes the existence and convergence of a variational scheme for modeling anisotropic surface diffusion with elasticity in the plane, extending previous methods to a more complex anisotropic setting.

Contribution

It introduces a new variational scheme inspired by Cahn-Taylor's approach, proving existence and convergence for anisotropic surface diffusion with elasticity in 2D.

Findings

Existence of classical solutions under regular initial conditions

Convergence of the scheme to the global solution

Extension of variational methods to anisotropic elastic surface diffusion

Abstract

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.