A uniqueness and stability principle for surface diffusion
Milan Kroemer, Tim Laux · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2026
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.