# Weak-strong uniqueness for the mean curvature flow of double bubbles

@inproceedings{Hensel2021WeakstrongUF, title={Weak-strong uniqueness for the mean curvature flow of double bubbles}, author={Sebastian Hensel and Tim Laux}, year={2021} }

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 construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478v2] for any such cluster. This extends the two-dimensional construction to the threedimensional case of surfaces meeting along triple junctions.

#### 2 Citations

On the existence of canonical multi-phase Brakke flows

- Mathematics
- 2021

This paper establishes the global-in-time existence of a multi-phase mean curvature flow, evolving from an arbitrary closed rectifiable initial datum, which is a Brakke flow and a BV solution at the… Expand

A new varifold solution concept for mean curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness

- Mathematics
- 2021

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 evolving varifolds,… Expand

#### References

SHOWING 1-10 OF 13 REFERENCES

Mean Curvature Flow with Triple Junctions in Higher Space Dimensions

- Physics, Mathematics
- 2012

We consider mean curvature flow of n-dimensional surface clusters. At (n−1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120°… Expand

Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions

- Mathematics
- 2008

We consider a system of three surfaces, graphs over a bounded domain in ℝ2, intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of… Expand

On the Surface Diffusion Flow with Triple Junctions in Higher Space Dimensions

- Physics, Mathematics
- Geometric Flows
- 2020

Abstract We show short time existence for the evolution of triple junction clusters driven by the surface diffusion flow. On the triple line we use the boundary conditions derived by Garcke and… Expand

A local regularity theorem for mean curvature flow with triple edges

- Mathematics, Physics
- 2016

Abstract Mean curvature flow of clusters of n-dimensional surfaces in ℝ n + k {\mathbb{R}^{n+k}} that meet in triples at equal angles along smooth edges and higher order junctions on… Expand

Convergence of the thresholding scheme for multi-phase mean-curvature flow

- Mathematics
- 2016

We consider the thresholding scheme, a time discretization for mean curvature flow introduced by Merriman et al. (Diffusion generated motion by mean curvature. Department of Mathematics, University… Expand

Existence of a lens-shaped cluster of surfaces self-shrinking by mean curvature

- Mathematics
- Mathematische Annalen
- 2019

We rigorously show the existence of a rotationally and centrally symmetric “lens-shaped” cluster of three surfaces, meeting at a smooth common circle, forming equal angles of $$120^{\circ }$$120∘,… Expand

Brakke’s inequality for the thresholding scheme

- Mathematics
- 2017

We continue our analysis of the thresholding scheme from the variational viewpoint and prove a conditional convergence result towards Brakke’s notion of mean curvature flow. Our proof is based on a… Expand

Calculus of Variations and Partial Differential Equations: Topics On Geometrical Evolution Problems And Degree Theory

- Mathematics
- 2000

I Geometric Evolution Problems.- Geometric evolution problems, distance function and viscosity solutions.- Variational models for phase transitions, an approach via ?-convergence.- Some aspects of De… Expand

Short-time existence for the network flow

- Mathematics
- 2021

This paper contains a new proof of the short-time existence for the flow by curvature of a network of curves in the plane. Appearing initially in metallurgy and as a model for the evolution of grain… Expand

On the mean curvature flow of grain boundaries

- Mathematics
- 2017

Suppose that $\Gamma_0\subset\mathbb R^{n+1}$ is a closed countably $n$-rectifiable set whose complement $\mathbb R^{n+1}\setminus \Gamma_0$ consists of more than one connected component. Assume that… Expand