论文标题
多相平均曲率流中能量景观的局部结构：弱的独特性和稳定性
The local structure of the energy landscape in multiphase mean curvature flow: Weak-strong uniqueness and stability of evolutions
论文作者
论文摘要
我们证明，在没有拓扑变化的情况下，BV溶液对平面多相平均曲率流的概念不允许（非物理）非唯一性的机制。我们的方法基于通过平均曲率在经典演变附近的能量景观的局部结构。平均曲率流是表面能函数的梯度流，我们开发了校准概念的梯度流类似物。就像存在校准的存在一样，可以确保人们在能源景观中达到了全球最小值一样，“梯度流量校准”的存在确保了能量景观中最陡峭下降的途径是独特而稳定的。
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.
