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

@article{Fischer2020TheLS, title={The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions}, author={Julian Fischer and Sebastian Hensel and Tim Laux and Thilo M. Simon}, journal={arXiv: Analysis of PDEs}, year={2020} }

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… Expand

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