Work

A uniqueness and stability principle for surface diffusion

Year: 2026

Type: article

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.

Source: Interfaces and Free Boundaries Mathematical Analysis Computation and Applications

DOI: 10.4171/ifb/575

Authors: Milan Kroemer, Tim Laux

Institutions: University of Bonn, Heidelberg University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, G591746060