15 citations · 42 across the 26 of their papers we have counts for
32 papers
De Giorgi varifold solutions to Mean Curvature Flow: a minimizing movements approach
Tim Laux, Andrea Poiatti
We propose an alternative existence proof of global weak solutions to mean curvature flow and volume preserving mean curvature flow. We prove for the first time for a minimizing mo…
Weak and strong solutions for a class of quasilinear Allen--Cahn systems
Harald Garcke, Tim Laux, Andrea Poiatti
We consider a quasilinear Allen--Cahn system which arises when the gradient energy term in the Ginzburg--Landau energy also contains zero order terms. Such systems offer significan…
Quantitative convergence of the nonlocal Allen--Cahn equation to volume-preserving mean curvature flow
Milan Kroemer, Tim Laux
We prove a quantitative convergence result of the nonlocal Allen--Cahn equation to volume-preserving mean curvature flow. The proof uses gradient flow calibrations and the relative…
Generic level sets in mean curvature flow are BV solutions
Anton Ullrich, Tim Laux
We show that a generic levelset of the viscosity solution to mean curvature flow is a distributional solution in the framework of sets of finite perimeter by Luckhaus and Sturzenhe…
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…
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…
Nematic-Isotropic phase transition in Liquid crystals: a variational derivation of effective geometric motions
Tim Laux, Yuning Liu
In this work, we study the nematic-isotropic phase transition based on the dynamics of the Landau--De Gennes theory of liquid crystals. At the critical temperature, the Landau--De…
The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions
Julian Fischer, Sebastian Hensel, Tim Laux +1
We prove that in the absence of topological changes, the notion of BV solutions to planar multiphase mean curvature flow does not allow for a mechanism for (unphysical) non-uniquen…
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…