The surface diffusion flow with elasticity in the plane

TL;DR

This paper proves the short-time existence and stability of solutions to a surface diffusion flow with elasticity in the plane, without needing extra curvature regularization.

Contribution

It establishes the first short-time existence and stability results for the elastic surface diffusion flow in the plane without additional regularization.

Findings

Proves short-time existence of smooth solutions.

Shows asymptotic stability of strictly stable stationary sets.

Addresses the flow without extra curvature regularization.

Abstract

In this paper we prove short-time existence of a smooth solution in the plane to the surface diffusion equation with an elastic term and without an additional curvature regularization. We also prove the asymptotic stability of strictly stable stationary sets.