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…