A uniqueness and stability principle for surface diffusion

Interfaces and Free Boundaries Mathematical Analysis Computation and Applications 2026 Open access

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Authors: Milan Kroemer, Tim Laux
DOI: 10.4171/ifb/575
Cited by: 0

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.

Fields of Study & Subjects

Advanced Mathematical Modeling in Engineering Nonlinear Partial Differential Equations Geometric Analysis and Curvature Flows

Publication details

Journal / source
Interfaces and Free Boundaries Mathematical Analysis Computation and Applications
Publication date
18 May 2026
Language
EN