15 citations · 42 across the 26 of their papers we have counts for
8 papers · 1 filter
Diffuse-interface approximation and weak-strong uniqueness of anisotropic mean curvature flow
Tim Laux, Kerrek Stinson, Clemens Ullrich
The purpose of this paper is to derive anisotropic mean curvature flow as the limit of the anisotropic Allen-Cahn equation. We rely on distributional solution concepts for both the…
A uniqueness and stability principle for surface diffusion
Milan Kroemer, Tim Laux
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…
Local minimizers of the interface length functional based on a concept of local paired calibrations
Julian Fischer, Sebastian Hensel, Tim Laux +1
We establish that regular flat partitions are locally minimizing for the interface energy with respect to perturbations of the phases. Regular flat partitions are partitions…
Large data limit of the MBO scheme for data clustering: convergence of the dynamics
Tim Laux, Jona Lelmi
We prove that the dynamics of the MBO scheme for data clustering converge to a viscosity solution to mean curvature flow. The main ingredients are (i) a new abstract convergence re…
Sharp Interface Limit of the Cahn-Hilliard Reaction Model for Lithium-ion Batteries
Tim Laux, Kerrek Stinson
We propose a weak solution theory for the sharp interface limit of the Cahn-Hilliard reaction model, a variational PDE for lithium-ion batteries. An essential feature of this model…
A phase-field version of the Faber--Krahn theorem
Paul Hüttl, Patrik Knopf, Tim Laux
We investigate a phase-field version of the Faber--Krahn theorem based on a phase-field optimization problem introduced in Garcke et al. [ESAIM Control Optim. Calc. Var. 29 (2023),…
Weak-strong uniqueness for volume-preserving mean curvature flow
Tim Laux
In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient…
Strong convergence of the thresholding scheme for the mean curvature flow of mean convex sets
Jakob Fuchs, Tim Laux
In this work, we analyze Merriman, Bence and Osher's thresholding scheme, a time discretization for mean curvature flow. We restrict to the two-phase setting and mean convex initia…