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math.AP2019
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…
math.AP2019
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…
math.AP2019
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…