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arXiv 2003.054782020-03math.AP

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

Julian Fischer, Sebastian Hensel, Tim Laux, Theresa Simon

备注：: 104 pages

英文摘要：

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.

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