2 citations · 4 across the 8 of their papers we have counts for
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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 new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness
Sebastian Hensel, Tim Laux
We propose a new weak solution concept for (two-phase) mean curvature flow which enjoys both (unconditional) existence and (weak-strong) uniqueness properties. These solutions are…
Weak-strong uniqueness for the mean curvature flow of double bubbles
Sebastian Hensel, Tim Laux
We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit cons…
Distributional solutions to mean curvature flow
Tim Laux
These lecture notes aim to present some of the ideas behind the recent (conditional) existence and (weak-strong) uniqueness theory for mean curvature flow. Focusing on the simplest…
De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions
Tim Laux, Jona Lelmi
We provide a new convergence proof of the celebrated Merriman-Bence-Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general cl…