A uniqueness and stability principle for surface diffusion

TL;DR

This paper establishes a principle ensuring uniqueness and stability of surface diffusion processes before singularities occur, accommodating topological changes and using a relative energy inequality with gradient flow calibrations.

Contribution

It introduces a novel stability and uniqueness principle for surface diffusion that handles topological changes and applies to various dimensions.

Findings

Proves a stability and uniqueness principle for surface diffusion.

Constructs explicit gradient flow calibrations for the analysis.

Applicable to stationary solutions in any dimension and smooth solutions in two dimensions.

Abstract

We derive a uniqueness and stability principle for surface diffusion before the onset of singularities. The perturbations, however, are allowed to undergo topological changes. The main ingredient is a relative energy inequality, which in turn relies on the explicit construction of (volume-preserving) gradient flow calibrations. The proof applies to stationary solutions in any dimension and to general smooth solutions in two dimensions.