A uniqueness and stability principle for surface diffusion
Analysis of PDEs
2023-10-24 v4
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.
Cite
@article{arxiv.2212.12487,
title = {A uniqueness and stability principle for surface diffusion},
author = {Milan Kroemer and Tim Laux},
journal= {arXiv preprint arXiv:2212.12487},
year = {2023}
}