The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions

Fischer, Julian L; Hensel, Sebastian; Laux, Tim; Simon, Thilo

The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions

Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv, 2003.05478.

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https://arxiv.org/abs/2003.05478 [Preprint]

Preprint | Submitted | English

Author

Fischer, Julian L^ISTA ; Hensel, Sebastian^ISTA ; Laux, Tim; Simon, Thilo

Department

Fischer Group

Grant

International IST Doctoral Program

Abstract

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-uniqueness. Our approach is based on the local structure of the energy landscape near a classical evolution by mean curvature. Mean curvature flow being the gradient flow of the surface energy functional, we develop a gradient-flow analogue of the notion of calibrations. Just like the existence of a calibration guarantees that one has reached a global minimum in the energy landscape, the existence of a "gradient flow calibration" ensures that the route of steepest descent in the energy landscape is unique and stable.

Publishing Year

2020

Date Published

2020-03-11

Journal Title

arXiv

Acknowledgement

Parts of the paper were written during the visit of the authors to the Hausdorff Research Institute for Mathematics (HIM), University of Bonn, in the framework of the trimester program “Evolution of Interfaces”. The support and the hospitality of HIM are gratefully acknowledged. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 665385.

Article Number

2003.05478

IST-REx-ID

10012

Cite this

Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv.

Fischer, J. L., Hensel, S., Laux, T., & Simon, T. (n.d.). The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv.

Fischer, Julian L, Sebastian Hensel, Tim Laux, and Thilo Simon. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” ArXiv, n.d.

J. L. Fischer, S. Hensel, T. Laux, and T. Simon, “The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions,” arXiv. .

Fischer JL, Hensel S, Laux T, Simon T. The local structure of the energy landscape in multiphase mean curvature flow: weak-strong uniqueness and stability of evolutions. arXiv, 2003.05478.

Fischer, Julian L., et al. “The Local Structure of the Energy Landscape in Multiphase Mean Curvature Flow: Weak-Strong Uniqueness and Stability of Evolutions.” ArXiv, 2003.05478.

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