论文标题
变形的新模型：线性失真和排名一凸的失败
New models for deformations: Linear Distortion and the failure of rank-one convexity
论文作者
论文摘要
在本文中，我们讨论了基于线性失真的标度不变的共形能量功能的静态非线性变形的新模型。特别是，我们举例说明，尽管估计值估计给紧凑，但最小化序列的能量将严格低于其极限，并且该能量差距可能很大。我们通过证明iWaniec的定理对线性映射的线性扭曲的等级 - 一个凸度的故障实际上是通用的，我们随后确定最佳的秩一个方向，以使线性映射变形以最大程度地减少其失真。
In this article, we discuss new models for static nonlinear deformations via scale-invariant conformal energy functionals based on the linear distortion. In particular, we give examples to show that, despite equicontinuity estimates giving compactness, minimising sequences will have strictly lower energy than their limit, and that this energy gap can be quite large. We do this by showing that Iwaniec's theorem on the failure of rank-one convexity for the linear distortion of a specific family of linear mappings, is actually generic and we subsequently identify the optimal rank-one direction to deform a linear map to maximally decrease its distortion.
