7 papers
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…
Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies
Julian Fischer, Tim Laux, Theresa M. Simon
We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter…
The thresholding scheme for mean curvature flow and de Giorgi's ideas for minimizing movements
Tim Laux, Felix Otto
We consider the thresholding scheme and explore its connection to De Giorgi's ideas on gradient flows in metric spaces; here applied to mean curvature flow as the steepest descent…
Mullins-Sekerka as the Wasserstein flow of the perimeter
Antonin Chambolle, Tim Laux
We prove the convergence of an implicit time discretization for the one-phase Mullins-Sekerka equation, possibly with additional non-local repulsion, proposed in [F. Otto, Arch. Ra…
Well-posedness for degenerate elliptic PDE arising in optimal learning strategies
Tim Laux, J. Miguel Villas-Boas
We derive a comparison principle for a degenerate elliptic partial differential equation without boundary conditions which arises naturally in optimal learning strategies. Our argu…
Implicit time discretization for the mean curvature flow of mean convex sets
Guido De Philippis, Tim Laux
In this note we analyze the Almgren-Taylor-Wang scheme for mean curvature flow in the case of mean convex initial conditions. We show that the scheme preserves strict mean convexit…