变形的新模型：线性畸变和秩一凸性的失效
New models for deformations: Linear Distortion and the failure of rank-one convexity
摘要：
在这篇文章中，我们讨论了新的模型的静态非线性变形的尺度不变的共形能量泛函的基础上的线性失真。特别是，我们给出的例子表明，尽管等度连续性的估计，使紧凑性，最小化序列将有严格低于其限制的能量，这个能量差距可以相当大。我们这样做，表明Iwaniec的定理失败的秩一凸的线性失真的一个特定的家庭的线性映射，实际上是通用的，我们随后确定的最佳秩一方向变形的线性映射，以最大限度地减少其失真。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
