Fischer, Julian and Hensel, Sebastian and Laux, Tim and Simon, Theresa M. (2025) The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. ISSN 1435-9855, 1435-9863
Full text not available from this repository. (Request a copy)Abstract
We prove that in the absence of topological changes, the notion of \operatorname{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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | IMPLICIT TIME DISCRETIZATION; CONVEX CALIBRABLE SETS; VISCOSITY SOLUTIONS; MOTION; EXISTENCE; JUNCTIONS; multiphase mean curvature flow; weak-strong uniqueness; varifold solutions; relative entropy method |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Tim Laux |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 18 Jun 2026 08:38 |
| Last Modified: | 18 Jun 2026 08:38 |
| URI: | https://pred.uni-regensburg.de/id/eprint/67007 |
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