15 citations · 42 across the 26 of their papers we have counts for
8 papers · 1 filter
BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness
Sebastian Hensel, Tim Laux
We study weak solutions to mean curvature flow satisfying Young's angle condition for general contact angles . First, we construct BV solutions using the Allen-Cahn app…
Large data limit of the MBO scheme for data clustering: -convergence of the thresholding energies
Tim Laux, Jona Lelmi
In this work we begin to rigorously analyze the MBO scheme for data clustering in the large data limit. Each iteration of the MBO scheme corresponds to one step of implicit gradien…
The Hele-Shaw flow as the sharp interface limit of the Cahn-Hilliard equation with disparate mobilities
Milan Kroemer, Tim Laux
In this paper, we study the sharp interface limit for solutions of the Cahn-Hilliard equation with disparate mobilities. This means that the mobility function degenerates in one of…
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…
Phase-Field Methods for Spectral Shape and Topology Optimization
Harald Garcke, Paul Hüttl, Christian Kahle +2
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is…
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…