The surface diffusion flow with elasticity in three dimensions

TL;DR

This paper proves the short-time existence and stability of solutions for the surface diffusion flow with elasticity in three dimensions, advancing understanding of elastic effects in geometric evolution equations.

Contribution

It establishes the first short-time existence results and stability analysis for the surface diffusion flow with elastic terms in three dimensions.

Findings

Proved short-time existence of smooth solutions.

Established asymptotic stability of strictly stable stationary sets.

Extended understanding of elastic effects in surface diffusion flows.

Abstract

We establish short-time existence of a smooth solution to the surface diffusion equation with an elastic term and without an additional curvature regularization in three space dimensions. We also prove the asymptotic stability of strictly stable stationary sets.